IMPMS 2026: THE 5TH ITALIAN MEETING ON PROBABILITY AND MATHEMATICAL STATISTICS

This page contains an index consisting of author-provided keywords.

2
2-state Markov modulated	On the Markov modulated Poisson process and its application in shock models
2D Euler equations	Refined uniqueness results for 2D Euler and gSQG with rough Kraichnan noise
A
A change-of-variable formula with local time on surfaces	Optimal autonomous trading strategies in models based on Ornstein-Uhlenbeck processes with mean-reverting levels
A priori estimates	Large field problem in coercive singular PDEs
Abatement technologies	Strategic Focus or Technological Neutrality? On the Optimal Mix of Green Investment and Carbon Capture and Storage Research in a Budget-Constraint World
Acceptance sets	Measuring Financial Resilience Using Backward Stochastic Differential Equations
adaptive Lasso regularization	Learning Interaction Networks for High-Dimensional Diffusion Processes
Additive Gaussian process regression	Computationally efficient hierarchical additive interaction models through hierarchical ANOVA kernels and Gaussian processes
Additive subordination	Multivariate additive subordination with applications in finance
Adjoint calculus	A Novel Approach to Peng's Maximum Principle for McKean-Vlasov Stochastic Differential Equations
Affine Volterra processes with jumps	Lévy processes as weak limits of rough Heston models
ageing	Branching Random Walks with ageing
Aldous-Hoover theorem	de Finetti Theorems for Constrained Exchangeable Graphs
Algebraic Quantum Field Theory	On the Stochastic Sine-Gordon Model from the Viewpoint of Quantum Field Theory
Algorithms for Dynamic Networks	Approximate 2-hop neighborhoods on incremental graphs: An efficient lazy approach
Allen–Cahn equations	Stochastic diffuse interface models driven by conservative noise
Almost Conditional Identical Distribution	Almost conditionally identically distributed random variables
Almost Supermartingale	Almost conditionally identically distributed random variables
Ambiguity	Robust Ergodic Singular Control of Compound–Poisson Jump Diffusions under Drift and Intensity Ambiguity
Analysis of PDEs	Recent Developments on Singular SPDEs in Heterogeneous Media and Curved Spaces
Anisotropic Gaussian fields	Limit theorems for space-time Gaussian fields on $\mathbb R^d$
Anomalous Diffusion	On some stochastic models of Anomalous Diffusion
Anomalous Dissipation	Anomalous Regularization and Dissipation for 2D Euler Equations with Rough Kraichnan Noise Non-selection of Lagrangian trajectories in the zero-noise limit Anomalous phenomena in the Kraichnan model of turbulence
Anomalous Regularization	Anomalous Regularization and Dissipation for 2D Euler Equations with Rough Kraichnan Noise Anomalous phenomena in the Kraichnan model of turbulence
Appell polynomials	Wick integrals
Approximate Bayesian Computation	Approximate Bayesian computation with kernel Wasserstein distance
ARL	An EWMA Control Chart to Monitor a Multivariate Binomial Process
Artificial Experts	Artificial Experts in Multi-Criteria Group Decision-Making
Association	Association in Spatial Queueing-Filtering Networks
assortativity	Bayesian Nonparametric Community Detection in Stochastic Block Models with Structural Constraints
assumption free	Conditional Coverage in Conformal Prediction: Tradeoffs and Insights
Asymptotic Behavior	Second Quantization and Evolution Operators in infinite dimension
Asymptotic estimates	Well-posedness results and asymptotic estimates for fractional partial differential equations
Asymptotic Theory	Asymptotic theory for the likelihood-based block maxima method in time series
Attractor properties	Long-time behaviour for birth-and-death dynamics in the continuum
B
backward stochastic differential equations	Measuring Financial Resilience Using Backward Stochastic Differential Equations Bismut-Elworthy type formulae for BSDEs with degenerate noise
Barycenter	Wasserstein Least Squares: statistics, geometry, and algorithms
Bayes Hilbert space	Functional PCA for Risk-Neutral densities in Bayes space
Bayesian asymptotics	Posterior behaviour of the stick-breaking weights for Bayesian infinte mixture models
Bayesian hierarchical modeling	Cognitive data analysis with Bayesian Drift Diffusion Model
Bayesian Inference	Accurate Bayesian inference for tail risk extrapolation in time series Asymptotic theory for the likelihood-based block maxima method in time series
Bayesian model selection	Adaptive variational Gaussian processes
Bayesian Neural Networks	Beyond NNGP: Large Deviations and Feature Learning in Bayesian Neural Networks
Bayesian nonparametrics	Separate Exchangeability as Modeling Principle in Bayesian Nonparametrics Hierarchical Random Measures without Tables Bayesian calculus and predictive characterizations of extended feature allocation models Computationally efficient hierarchical additive interaction models through hierarchical ANOVA kernels and Gaussian processes Bayesian Nonparametric Community Detection in Stochastic Block Models with Structural Constraints Exchangeable random permutations with an application to Bayesian graph matching A partial likelihood approach to tree-based density modeling and its application in Bayesian inference Dynamic network clustering via connectivity pattern persistence and node-level dependence
Bayesian predictive inference	Asymptotic and empirical properties of some classes of predictive distribution
Bayesian Statistics	Almost conditionally identically distributed random variables
Bayesian supervised learning	Edgeworth Expansions and Non-Gaussian Corrections in Finite-Width Wide Neural Networks
Beacon-based monitoring	New Distributed Beacon-Based Approaches for Multi-Parameter Monitoring: Sentinel-GRID
Bead model	The bead model and the macroscopic behaviour of Gelfand-Tsetlin patterns
Belief functions	Reinsurance games through quantile-constrained Choquet-Wasserstein approximations
beneficial exchanges	Does cooperation improve individual performance?
Bernstein functions	Fractional Calculus and Gaussian Processes: extensions and alternatives to fractional Brownian motion
Bernstein–von Mises theorem	Predictive Bernstein-von Mises Theorems
Bessel functions	Directed polymer in spatially correlated environment
Bilevel Optimization	ZOBA: An Efficient Single-loop Zeroth-order Bilevel Optimization Algorithm
Binomial catastrophes	Capturing Growth and Shock Dynamics through Lognormal Diffusions with Binomial Catastrophes
Biological application	Capturing Growth and Shock Dynamics through Lognormal Diffusions with Binomial Catastrophes
Black-box Optimization	ZOBA: An Efficient Single-loop Zeroth-order Bilevel Optimization Algorithm
Block Maxima	Asymptotic theory for the likelihood-based block maxima method in time series
Boltzmann	Boltzmann processes
Boltzmann Energy	Global Optimization via Softmin Energy Minimization
Boltzmann-Grad limit	Random Flights and Anomalous Diffusion: A non-Markovian Take on Lorentz Processes
Bootstrap	Inference for a concave distribution function under measurement error
Bouncing drift	Measuring Financial Resilience Using Backward Stochastic Differential Equations
branching process	Branching Random Walks with ageing
branching random walk	Branching Random Walks with ageing
Bregman divergence
Brownian motion	The Dubins Constants for Walsh's Spider Process
Brownian motions	Non-local dynamic boundary conditions for sticky Brownian motions on smooth domains
BSDEs	Relative Performance Concerns in Financial Markets under Recursive Intertemporal Preferences
budget renewals	Target hitting counting process in networks and applications to evanescent random walks
C
c-quasi-convex	Robust quasi-convex and cash-subadditive risk measures: theory, duality, and applications
Cahn–Hilliard equations	Stochastic diffuse interface models driven by conservative noise
capacity	Solidification estimates for random walks on supercritical percolation clusters
Caputo fractional derivative	Non-local operators for Pearson diffusions
car-sharing	Large-Scale Analysis of Multi-Scale Queuing Networks: Applications to Car-Sharing Systems
Cash-subadditive	Robust quasi-convex and cash-subadditive risk measures: theory, duality, and applications
Categorical Data Analysis	The Reverse Hypergeometric distribution for attribute concentration in small groups
Central and non central limit theorems	Non-universal fluctuations for functionals of random neural networks
Central Limit Theorem	Directed polymer in spatially correlated environment
Centrality measures	Payment-failure times for random Lightning paths
cephoids	The geometry of the stability region of randomly modulated queuing systems
Change of Measure	Strong disorder for Stochastic Heat Flow and 2D Directed Polymers
Change point detection	Optimal Annuitization under Partially Observable Mortality
Cheeger constant	Estimate of the exit time for the Long Range Ising model on random regular graphs
Chemical reaction networks	Noise induced stabilization in stochastic chemical reaction network
classification	Conformal classification with tight marginal coverage in noisy settings
cliques	Homophily within and across groups: a maximum-entropy framework for analyzing different social scales
closed convex cone	Invariant cones for jump-diffusions in infinite dimensions
Cluster Formation	Reduced stochastic PDE models for collective behaviour
clustering	A multiscale analysis of mean-field transformers in the moderate interaction regime Posterior behaviour of the stick-breaking weights for Bayesian infinte mixture models
Co-evolution	Infection models on dense dynamic random graphs
Coalescent process	Large-sample asymptotics of coalescent importance sampling algorithms
Coarse-Graining	Strong disorder for Stochastic Heat Flow and 2D Directed Polymers
Coherence
Coherent systems	Analysis of Systems through the Regression Importance Signature
Collective Arbitrage	Collective Arbitrage and Superreplication
Collective arbitrage theory	Does cooperation improve individual performance?
Collective behaviour	Reduced stochastic PDE models for collective behaviour
Collective FTAP	Collective completeness and pricing hedging duality
Collective Superreplication	Collective Arbitrage and Superreplication
Combinatorics	The Reverse Hypergeometric distribution for attribute concentration in small groups
Common noise	Existence of Strong Randomized Equilibria in Mean-Field Games of Optimal Stopping with Common Noise Fast-slow mean-field games with common noise
community detection	Simultaneous global and local clustering in multiplex networks with covariate information Localized geometry detection in scale-free random graphs Bayesian Nonparametric Community Detection in Stochastic Block Models with Structural Constraints
community structure	Homophily within and across groups: a maximum-entropy framework for analyzing different social scales
compact support	The moment problem beyond finite dimensions
Competing growth	Competing growth on the configuration model via first-passage percolation and long-range jumps
Competitive displacement	The grass-bushes-trees process on a scale-free network
complementary set partitions	Efficient computation and estimation of generalized cumulants via complementary set partitions
Completely monotone kernels	Stochastic Volterra Equations on Convex Domains
Completely random measure	Hierarchical Random Measures without Tables
Completeness	Collective completeness and pricing hedging duality
Complex systems	A fractional Hawkes process
Complexity	Ordering and measuring the complexity of lotteries Learning with Neural Networks on Structured Inputs
Compound Conditionals	Multi-Criteria Decision-Making, Conditional Probabilities, and Fuzzy Sets
Compressible fluids	Invariant measures for one-dimensional stochastic compressible fluid equations
Concentration bound	Nonlocal α-size biasing: Stein characterization and one-sided concentration bound
Concentration of the degree sequence	Do random initial degrees suppress concentration in preferential attachment graphs?
conditional coverage	Conditional Coverage in Conformal Prediction: Tradeoffs and Insights
conditional diffusion models	Dimension-free statistical guarantees for fine-tuning of conditional diffusion models via PAC-Bayes bounds
Conditional expectation	de Finetti theorem for quantum stochastic processes based on twisted products: conditional independence
Conditional Identical Distribution	Almost conditionally identically distributed random variables
Conditional identity in distribution	Exchangeable measure-valued Pólya sequences Asymptotic and empirical properties of some classes of predictive distribution
Conditional independence	de Finetti theorem for quantum stochastic processes based on twisted products: conditional independence
Conditional partial exchangeability	Dynamic network clustering via connectivity pattern persistence and node-level dependence
Conditional Random Quantities	Multi-Criteria Decision-Making, Conditional Probabilities, and Fuzzy Sets
Conditionally Gaussian Random variables	Edgeworth Expansions and Non-Gaussian Corrections in Finite-Width Wide Neural Networks
Configuration model	Competing growth on the configuration model via first-passage percolation and long-range jumps
conformal inference	Distribution-Free Outlier Detection and Enumeration Conformal classification with tight marginal coverage in noisy settings
conformal prediction	A Conformal Prediction Approach to Predict Populations of Graphs Conditional Coverage in Conformal Prediction: Tradeoffs and Insights
Conjunction and disjunction
Connectivity threshold	Finite vs Infinite-Mean Heavy-Tailed Fitness: Geometry and Connectivity in Inhomogeneous Random Graphs
Consensus Dynamics	The Minority Dynamics
conservative noise	Stochastic diffuse interface models driven by conservative noise
Constrained estimation	Inference for a concave distribution function under measurement error
Constrained-decoding	Modeling Vagueness in Large Language Models: A Hybrid Logical-Probabilistic Perspective on Moral Classification and Constrained Generation
Constraints	Strategic Focus or Technological Neutrality? On the Optimal Mix of Green Investment and Carbon Capture and Storage Research in a Budget-Constraint World
contact process	Contact process on interchange process
Context-Dependent Decision-Making	A Quantum-Probabilistic Framework for Decision-Making under Vagueness
Contextual Uncertainty	A Quantum-Probabilistic Framework for Decision-Making under Vagueness
Continuous time Markov chains	Noise induced stabilization in stochastic chemical reaction network Generalizations of Elastic Brownian Motion
continuous time random walk	Laplace's first law of errors applied to Markov and non-Markov diffusive motion
continuous-time Markov chain	Stochastic ordering tools for reaction network models
Continuous-Time Markov Chains	Stability of Reaction Networks with Randomly Switching Parameters - part 2 Stability of Reaction Networks with Randomly Switching Parameters - Part 1
Continuous-time random walks	Master Equations for Continuous-Time Random Walks with Stochastic Resetting
contraction rates	Adaptive variational Gaussian processes
Contributed Session	Nonparametric Inference for Multivariate and Complex Data Structures
convergence	Numerical Approximation of McKean-Vlasov SDEs via Stochastic Gradient Descent
Convergence analysis	Theoretical guarantees for diffusion models — beyond log-concavity
Convergence Guarantees	Exponential Convergence Guarantees for Iterative Markovian Fitting
Convergence of probability measures	Asymptotic and empirical properties of some classes of predictive distribution
convergence problem	Convergence for linear quadratic potential mean field games
convex monotone semigroup	An optimal transport foundation for a class of dynamically consistent risk measures
convolution equivalence	Thorin processes: subordination and applications
Convolution-type derivative	Time-changed random evolutions and fractional hyperbolic-type equations
Cooperation	Collective completeness and pricing hedging duality
core-periphery	Bayesian Nonparametric Community Detection in Stochastic Block Models with Structural Constraints
Correlated environment	Pinning polymer model in correlated random environment
correlated stochastic blockmodel	Exchangeable random permutations with an application to Bayesian graph matching
Correlation	Correlation Structure for Random Waves
Cox process	Bayesian nonparametric inference for covariate-driven point processes
Cox-Ingersoll-Ross model	Singular SDEs through interfaces: the threshold Cox-Ingersoll-Ross model
critical parameters	Branching Random Walks with ageing
critical points	Critical Points and Euler characteristic for Time-Dependent Spherical Random Fields
Critical space-correlation	Directed polymer in spatially correlated environment
critical stochastic heat flow	Moment structure of the critical stochastic heat flow and independence of collision times of random walks
criticality	A stochastic volatility approximation for a tick-by-tick price model with mean-field interaction
cryo-EM	Low-Dose Tomography of Random Fields and the Problem of Continuous Heterogeneity
Cubature scheme	Guidelines for Cubature-based Likelihood approximation of 3D Poisson Point Processes
Cucker-Smale	Reduced stochastic PDE models for collective behaviour
Cumulative shock model	On the Markov modulated Poisson process and its application in shock models
cutoff phenomenon	Mixing trichotomy for random walks on directed stochastic block models
D
Data over Audio	New Distributed Beacon-Based Approaches for Multi-Parameter Monitoring: Sentinel-GRID
Data Sketches	Approximate 2-hop neighborhoods on incremental graphs: An efficient lazy approach Maintaining k-MinHash Signatures over Fully-Dynamic Data Streams with Recovery
de Finetti priors	de Finetti Theorems for Constrained Exchangeable Graphs
De Morgan’s law
Dean-Kawasaki equation	Entropic Regularization of Rearranged Stochastic Heat Equation
Dean–Kawasaki	Reduced stochastic PDE models for collective behaviour
Dean–Kawasaki equation	Massive Particle Systems, Wasserstein Brownian Motions, and the Dean--Kawasaki SPDE
Decision Theory	Disappointment aversion and expectiles
Deconvolution	Inference for a concave distribution function under measurement error
Deep Galerkin method	Deep Hilbert Galerkin methods for PDEs on Hilbert spaces via derivative-informed operator learning with applications to stochastic optimal control of infinite-dimensional systems Derivative-informed Hilbert neural operators solve PDEs on Hilbert spaces and infinite-dimensional optimal control problems
Deep Learning	Mean-Field Optimal Control Approach to Deep Learning
deep neural networks	Spectral and Geometric Phase Transitions in Deep Neural Networks Deep Transformers as Mean-field Interacting Particle Systems
Degenerate noise	Strong Feller property and irreducibility for stochastic PDEs with degenerate multiplicative noise Bismut-Elworthy type formulae for BSDEs with degenerate noise
deGua simplices	The geometry of the stability region of randomly modulated queuing systems
denoising diffusion models	Adaptive denoising diffusion modelling via random time reversal
Density Estimation	A partial likelihood approach to tree-based density modeling and its application in Bayesian inference
Dependence Measure	Hilbert-Based Correlation Indices for Distributional Data
deposition model	A jewel and two dials in the ideal Poisson--Voronoi tessellation
Deterministic equivalent	Learning from Surrogate Data: Weak-to-Strong Generalization through the Lens of High-Dimensional Regression
diffusion in disordered medium	Laplace's first law of errors applied to Markov and non-Markov diffusive motion
Diffusion models	Theoretical guarantees for diffusion models — beyond log-concavity Algorithm- and Data-Dependent Generalization Bounds for Diffusion Models
Diffusion process	Approximation of Diffusion Exit Times from Bounded Domains via a Rejection-Based Random Walk
Diffusion processes	First-passage times through closed curves for bivariate diffusion processes, simulations and comparisons based on stochastic orderings Nonparametric Estimation of the Diffusive Interaction Function in Particle Systems
Diffusion with resetting	Can the introduction of resetting expedite the first passage of a diffusion process?
Directed Polymer in Random Environment	Strong disorder for Stochastic Heat Flow and 2D Directed Polymers Directed polymer in spatially correlated environment
directed polymer in random environments	Moment structure of the critical stochastic heat flow and independence of collision times of random walks
Directed polymers	Noise sensitivity and directed polymers
Dirichlet process	Hierarchical Random Measures without Tables
Dirichlet–Ferguson measure	PDEs driven by Dirichlet-Ferguson laplacian in Wasserstein-Sobolev spaces
Disappointment aversion	Disappointment aversion and expectiles
Discrete curvature	Exploring the space of graphs with fixed discrete curvatures
discrete diffusion models	Non-Asymptotic Convergence of Discrete Diffusion Models: Masked and Random Walk dynamics
Discrete Laplacians	Random evolution on combinatorial and metric graphs
Discrete Probability Distribution	The Reverse Hypergeometric distribution for attribute concentration in small groups
discretionary stopping	Mean field games with option to buy information
Discretization	Sampling error bounds for the denoising diffusion probabilistic model via the Föllmer process
disorder	Metastability of Glauber dynamics with inhomogeneous coupling disorder
Disorder (change-point) problem	The Wiener Disorder Problem with Random Post-Disorder Drift
Disordered Systems	Strong disorder for Stochastic Heat Flow and 2D Directed Polymers Directed polymer in spatially correlated environment
Distributed Algorithms	Threshold-Driven Streaming Graph: Expansion and Rumor Spreading The Minority Dynamics
Distributional symmetries	On the Ryll-Nardzewski Theorem for Quantum Stochastic Processes
Donsker classes	Two-sample test for laws of random probabilities via optimal transport
Drift-based transformations	On some drift-based transformations of multidimensional diffusion processes and their applications
Drift-diffusion models	Cognitive data analysis with Bayesian Drift Diffusion Model
duality	Gamma duality and a tractable transition density for the Wright-Fisher diffusion with selection
Dubins constants	The Dubins Constants for Walsh's Spider Process
Dynamic Algorithms	Maintaining k-MinHash Signatures over Fully-Dynamic Data Streams with Recovery
Dynamic boundary conditions	Non-local dynamic boundary conditions for sticky Brownian motions on smooth domains
Dynamic boundary value problems	Sticky vertices with energy accumulation
dynamic graph	The critical percolation window in growing random graphs
Dynamic networks	Poisson Hail on a Wireless Ground
dynamic programming equation in Wasserstein space	Optimal control of McKean-Vlasov systems under partial observation and hidden Markov switching
Dynamic Random Graphs	Do random initial degrees suppress concentration in preferential attachment graphs? Threshold-Driven Streaming Graph: Expansion and Rumor Spreading
dynamic risk measure	An optimal transport foundation for a class of dynamically consistent risk measures
Dynamic risk measures	Measuring Financial Resilience Using Backward Stochastic Differential Equations
Dynamical Mean Field Theory (DMFT)	ResNets of All Shapes and Sizes: Quantitative Large-Scale Theory of Training Dynamics
Dynamical system	Learning ergodic dynamical systems from finite trajectories
dynamics	Mean field optimal stopping and related N -player cooperative games
E
Edgeworth expansion	Edgeworth Expansions and Non-Gaussian Corrections in Finite-Width Wide Neural Networks
Elastic Brownian Motion	Generalizations of Elastic Brownian Motion
Elliptic-type free-boundary problem	Optimal autonomous trading strategies in models based on Ornstein-Uhlenbeck processes with mean-reverting levels
Empirical Bayes	Accurate Bayesian inference for tail risk extrapolation in time series
Empirical process	Testing for Multivariate Regular Variation
Empirical Risk Minimization	A Risk Minimization Approach to PCA with Irregular Data
ends	A jewel and two dials in the ideal Poisson--Voronoi tessellation
Energy balance model	Ergodicity of a Stochastic Energy Balance Model for Global Temperature
Ensemble optimal control	Normalizing Flows as Approximations of the Optimal Transport Map
Entropic Optimal Transport	A semiconcavity approach to stability of entropic plans and exponential convergence of Sinkhorn's algorithm - Part 2 A semiconcavity approach to stability of entropic plans and exponential convergence of Sinkhorn’s algorithm - Part 1
Entropic stability	A semiconcavity approach to stability of entropic plans and exponential convergence of Sinkhorn's algorithm - Part 2 A semiconcavity approach to stability of entropic plans and exponential convergence of Sinkhorn’s algorithm - Part 1
Entropy	A stochastic approach to time-dependent BEC
Entropy dissipation	Long-time behaviour for birth-and-death dynamics in the continuum
Environmental asset	Environmental asset, Optimal control, N-players game, Social Planner, Pigouvian tax, Mean field game
equation	Boltzmann processes
Erdos-Taylor theorem	Moment structure of the critical stochastic heat flow and independence of collision times of random walks
Ergodic decomposition	de Finetti Theorems for Constrained Exchangeable Graphs
Ergodic singular control	Robust Ergodic Singular Control of Compound–Poisson Jump Diffusions under Drift and Intensity Ambiguity
Ergodicity	Ergodicity of a Stochastic Energy Balance Model for Global Temperature
Euclidean field theory	The forward-backward approach to interacting fermionic states on the lattice
Euler Equations	Anomalous Regularization and Dissipation for 2D Euler Equations with Rough Kraichnan Noise
Euler Scheme \and	Efficient simulation of a new class of Volterra-type SDEs
Evolution equations in random environments	Random evolution on combinatorial and metric graphs
Evolution Operators	Second Quantization and Evolution Operators in infinite dimension
EWMA control chart	An EWMA Control Chart to Monitor a Multivariate Binomial Process
Exact prices	Parametric local volatility: Exact prices lead to sound continuous Markovian models
Exchangeability	Almost conditionally identically distributed random variables Exchangeable measure-valued Pólya sequences Dice processes, moment duality, and the propagation of exchangeability The Reverse Hypergeometric distribution for attribute concentration in small groups
exchangeable permutation probability function	Exchangeable random permutations with an application to Bayesian graph matching
Exclusion process	The bead model and the macroscopic behaviour of Gelfand-Tsetlin patterns Contact process on interchange process
Exclusion processes	Scaling limits of the one-dimensional facilitated exclusion process
excursion set	Critical Points and Euler characteristic for Time-Dependent Spherical Random Fields
Existence and uniqueness	Singular SDEs through interfaces: the threshold Cox-Ingersoll-Ross model
Exit problem	Approximation of Diffusion Exit Times from Bounded Domains via a Rejection-Based Random Walk
Expectiles	Integrated expectile-based measures of inequality Disappointment aversion and expectiles
Expert judgments	An Application of Fuzzy Set Theory and Interval-Based Distances for Expert Judgment Aggregation
Exponential expansion series	Functional PCA for Risk-Neutral densities in Bayes space
Exponential integrability	Exponential integrability of the solution and the invariant measure to the stochastic Burgers equation
Exponential random graphs	Exponential Random Edge-Colored Graphs via Probability Graphons: Free Energies and Extremal Colorings
exponential utility	On consistency of optimal portfolio choice for state-dependent exponential utilities
Extended Kalman-Bucy filtering model	Optimal autonomous trading strategies in models based on Ornstein-Uhlenbeck processes with mean-reverting levels
Extremal combinatorics	Exponential Random Edge-Colored Graphs via Probability Graphons: Free Energies and Extremal Colorings
Extreme shock model	On the Markov modulated Poisson process and its application in shock models
Extreme Value Theory	Asymptotic theory for the likelihood-based block maxima method in time series
Extreme Values	Extreme value statistics for partial orders
Extropy
F
Fast mean reversion	Lévy processes as weak limits of rough Heston models
Feature Interactions	A multi-factorial innovation model with feature-interaction
Feller semigroups	Random Flights and Anomalous Diffusion: A non-Markovian Take on Lorentz Processes
Feller test for explosion	Explosions of stochastic Volterra equations
Finance	Multivariate additive subordination with applications in finance
Financial crisis	Capturing Growth and Shock Dynamics through Lognormal Diffusions with Binomial Catastrophes
Financial resilience	Measuring Financial Resilience Using Backward Stochastic Differential Equations
Financial time series	Self-normalization of sums of dependent random variables
First passage time	Approximation of first passage times and hitting times for stochastic differential equations Optimal autonomous trading strategies in models based on Ornstein-Uhlenbeck processes with mean-reverting levels
First-exit time	Can the introduction of resetting expedite the first passage of a diffusion process?
First-passage time	Can the introduction of resetting expedite the first passage of a diffusion process?
First-passage-time problems	First-passage times through closed curves for bivariate diffusion processes, simulations and comparisons based on stochastic orderings
Flory–Huggins potential	Stochastic diffuse interface models driven by conservative noise
flow equation	Flow equation approach to stochastic quantisation
Fluctuating Hydrodynamics	Reduced stochastic PDE models for collective behaviour
Foias-Prodi estimates	Existence, uniqueness and asymptotic stability of invariant measures for the stochastic Allen–Cahn–Navier–Stokes system with singular potential
Fokker Plank equation	Mean field games in Hilbert spaces
Fokker--Planck Equation	Mean-Field Games in Hilbert Spaces: A Viscosity Approach
Fokker-Planck equations	Nonlinear Rough Fokker-Planck Equations
Fokker-Planck PDE	A non-local singular McKean SDE
Forman-Ricci curvature	Exploring the space of graphs with fixed discrete curvatures
forward performance	On consistency of optimal portfolio choice for state-dependent exponential utilities
Fr\'echet-Shohat Theorem	An Analogue Fr\'echet-Shohat Moments Convergence Theorem for Indeterminate Moment Problems
Fractional Brownian motion	Fractional Calculus and Gaussian Processes: extensions and alternatives to fractional Brownian motion Averaging Dynamics and Wong-Zakai approximations for a Fast-Slow Navier-Stokes System Driven by fractional Brownian Motion Non-selection of Lagrangian trajectories in the zero-noise limit Statistical inference for interacting particle systems driven by the fractional Brownian motion
Fractional Calculus	Generalizations of Elastic Brownian Motion
Fractional Cointegration	Fractional Cointegration of Geometric Functionals
Fractional derivative	Parameter estimation in a fractional neuronal model
Fractional Evolution Equations	Well-posedness results and asymptotic estimates for fractional partial differential equations
Fractional Integrals \and	Efficient simulation of a new class of Volterra-type SDEs
Free boundary	Mean field optimal stopping and related N -player cooperative games
Free boundary problem	Scaling limits of the one-dimensional facilitated exclusion process
Free probability	The bead model and the macroscopic behaviour of Gelfand-Tsetlin patterns
Fréchet-Hoeffding Bounds	Multi-Criteria Decision-Making, Conditional Probabilities, and Fuzzy Sets
Fréchet-Hoeffding bounds
Full and partial information	Optimal autonomous trading strategies in models based on Ornstein-Uhlenbeck processes with mean-reverting levels
Functional central limit theorems	Predictive Bernstein-von Mises Theorems
functional data analysis	Functional marked self-exciting point process models
Functional delta method	Inference for a concave distribution function under measurement error
functional integration	Stochastic Differential Equations and the Martin-Siggia-Rose Formalism: An Algebraic-Analytic Correspondence
Functional principal component analysis	Functional PCA for Risk-Neutral densities in Bayes space
Fuzzy distance	An Application of Fuzzy Set Theory and Interval-Based Distances for Expert Judgment Aggregation
Fuzzy Logic System	Optimizing Fuzzy Partitions for Visual Sensors
Fuzzy Method	Artificial Experts in Multi-Criteria Group Decision-Making
Fuzzy Multi-Expert Decision-Making	Artificial Experts in Multi-Criteria Group Decision-Making
Fuzzy Ontology	Artificial Experts in Multi-Criteria Group Decision-Making
Fuzzy set theory	An Application of Fuzzy Set Theory and Interval-Based Distances for Expert Judgment Aggregation
Fuzzy Sets	Multi-Criteria Decision-Making, Conditional Probabilities, and Fuzzy Sets
G
Galves-Löcherbach processes	{Macro-Micro Inference for Galves-Löcherbach Processes: Robust Synaptic Classification via Spike-Triggered Extrapolation
Gaussian field	Random scars : overview and recent advances
Gaussian fields	Non-universal fluctuations for functionals of random neural networks Statistics on Yau's conjecture
Gaussian free field	Hard wall repulsion for the discrete Gaussian free field in random environment in supercritical dimension
Gaussian initialization	Edgeworth Expansions and Non-Gaussian Corrections in Finite-Width Wide Neural Networks
Gaussian prior	Bayesian nonparametric inference for covariate-driven point processes
Gaussian Processes	Quantitative Convergence of Trained Quantum Neural Networks to a Gaussian Process Adaptive variational Gaussian processes Beyond NNGP: Large Deviations and Feature Learning in Bayesian Neural Networks Bayesian nonparametric estimation of spatio-temporal Hawkes processes
Gaussian random fields	Spectral and Geometric Phase Transitions in Deep Neural Networks
Gaussian Rough Paths	Averaging Dynamics and Wong-Zakai approximations for a Fast-Slow Navier-Stokes System Driven by fractional Brownian Motion
Gaussian states	Some structural results for Gaussian Quantum Markov Semigroups
Gelfand-Tsetlin pattern	The bead model and the macroscopic behaviour of Gelfand-Tsetlin patterns
Generalised Pareto	Accurate Bayesian inference for tail risk extrapolation in time series
Generalization Bounds	Algorithm- and Data-Dependent Generalization Bounds for Diffusion Models
generalization errors	Dimension-free statistical guarantees for fine-tuning of conditional diffusion models via PAC-Bayes bounds
Generalized cumulants	Efficient computation and estimation of generalized cumulants via complementary set partitions
Generalized fractional operators	Fractional Calculus and Gaussian Processes: extensions and alternatives to fractional Brownian motion
generalized gamma convolutions	Thorin processes: subordination and applications
Generalized Ising Model	On the Lyapunov exponent of discrete and continuum generalized Ising-models
Generalized Mehler semigroups	Hypercontractivity type property for generalized Mehler semigroups
generalized negative binomial convolutions	Thorin processes: subordination and applications
generalized SQG equations	Refined uniqueness results for 2D Euler and gSQG with rough Kraichnan noise
Generative interest rate modeling	Modeling with neural SPDEs: data-driven Heath-Jarrow-Morton models
Generative Models	Exponential Convergence Guarantees for Iterative Markovian Fitting On Forgetting and Stability of Score-based Generative models A partial likelihood approach to tree-based density modeling and its application in Bayesian inference
generative models for discrete data	Non-Asymptotic Convergence of Discrete Diffusion Models: Masked and Random Walk dynamics
Generator	Measuring Financial Resilience Using Backward Stochastic Differential Equations
Geometric Functionals	Fractional Cointegration of Geometric Functionals
Geometry	Recent Developments on Singular SPDEs in Heterogeneous Media and Curved Spaces
Gibbs measures	Long-time behaviour for birth-and-death dynamics in the continuum
Gibbs measures on infinite dimensional spaces	On the uniqueness of reversible invariant measures for SPDEs on the full space
Gibbs-type prior	Bayesian Nonparametric Community Detection in Stochastic Block Models with Structural Constraints
Glauber dynamics	Estimate of the exit time for the Long Range Ising model on random regular graphs Metastability of Glauber dynamics with inhomogeneous coupling disorder
Gradient descent	Learning with Neural Networks on Structured Inputs Mean-Field Optimal Control Approach to Deep Learning
gradient estimates	Bismut-Elworthy type formulae for BSDEs with degenerate noise
Graph dynamics	Infection models on dense dynamic random graphs
Graph Expansion	Threshold-Driven Streaming Graph: Expansion and Rumor Spreading
Graph limits	Probability graphons and large deviations for random weighted graphs Exponential Random Edge-Colored Graphs via Probability Graphons: Free Energies and Extremal Colorings
Graph Mining	Approximate 2-hop neighborhoods on incremental graphs: An efficient lazy approach
Graph parameters	de Finetti Theorems for Constrained Exchangeable Graphs
graph recovery	Learning Interaction Networks for High-Dimensional Diffusion Processes
Graphons	de Finetti Theorems for Constrained Exchangeable Graphs Convergence of subgraph densities in ERGMs
Greedy Independent set	Hydrodynamic limits of exploration processes on large random graphs
Greedy matching	Hydrodynamic limits of exploration processes on large random graphs
Gromov boundary	A jewel and two dials in the ideal Poisson--Voronoi tessellation
growing graph	The critical percolation window in growing random graphs
H
Hamilton--Jacobi--Bellman Equation	Mean-Field Games in Hilbert Spaces: A Viscosity Approach
hard wall	Hard wall repulsion for the discrete Gaussian free field in random environment in supercritical dimension
Hawkes	Efficient Simulation of Affine Volterra Processes
Hawkes process	Modeling Monkeypox transmission through stochastic dynamics with self-excitation
Hawkes processes	A stochastic volatility approximation for a tick-by-tick price model with mean-field interaction A fractional Hawkes process
heat equation	A multiscale analysis of mean-field transformers in the moderate interaction regime
Heat flow	Properties of diffusion transport maps via creation of log-semiconcavity along heat flows
Heath-Jarrow-Morton framework	Real-world models for multiple term structures: a unifying HJM semimartingale framework
Heath-Jarrow-Morton models	Modeling with neural SPDEs: data-driven Heath-Jarrow-Morton models
Heavy tails	Do random initial degrees suppress concentration in preferential attachment graphs? Random walks with stochastic resetting in complex networks
Heavy-tailed fitness	Finite vs Infinite-Mean Heavy-Tailed Fitness: Geometry and Connectivity in Inhomogeneous Random Graphs
Heisenberg group	Berry-Heisenberg random waves
Heston	Efficient Simulation of Affine Volterra Processes
Heterogeneous interaction	Mean-field control of heterogeneous systems
Hierarchical sample	Two-sample test for laws of random probabilities via optimal transport
High-dimensional regression	Learning from Surrogate Data: Weak-to-Strong Generalization through the Lens of High-Dimensional Regression
High-dimensional statistics	Nonparametric Estimation of the Diffusive Interaction Function in Particle Systems
High-frequency eigenfunctions	Statistics on Yau's conjecture
Hilbert space	Mean field games in Hilbert spaces
Hitting time on networks	Random walks with stochastic resetting in complex networks
Hitting times	Approximation of first passage times and hitting times for stochastic differential equations
HJB equation	Mean field games in Hilbert spaces
HJB equations	When investors force the green transition: a two-dimensional singular stochastic control problem
Hoermander theorem	Malliavin Calculus for rough stochastic differential equations
homophily	Homophily within and across groups: a maximum-entropy framework for analyzing different social scales
Hydrodynamic limit	Scaling limits of the one-dimensional facilitated exclusion process
Hydrodynamic limits	Hydrodynamic limits of exploration processes on large random graphs
Hypercontractivity	Hypercontractivity type property for generalized Mehler semigroups
Hypercontractivity Property	Second Quantization and Evolution Operators in infinite dimension
Hypergraphs	Constructing heavy-tailed directed hypergraphs
Hypocoercivity	On spectral gaps of stochastic wave equations
Hypothesis test	Testing for Multivariate Regular Variation
Hypothesis Testing	The Reverse Hypergeometric distribution for attribute concentration in small groups
I
identifiability conditions	Learning Interaction Networks for High-Dimensional Diffusion Processes
Implied volatility	Parametric local volatility: Exact prices lead to sound continuous Markovian models
Importance measures	Analysis of Systems through the Regression Importance Signature
Importance sampling	Large-sample asymptotics of coalescent importance sampling algorithms
Imprecise probability
incomplete information	Optimal resource extraction with a random threshold Mean field games with option to buy information
Indeterminate Moment Problem	An Analogue Fr\'echet-Shohat Moments Convergence Theorem for Indeterminate Moment Problems
Indian Buffet Process	A multi-factorial innovation model with feature-interaction Bayesian calculus and predictive characterizations of extended feature allocation models
indifference substitution	Event Valence and Subjective Probability
Inequality indices	Integrated expectile-based measures of inequality
Inference	Linearization of McKean SDEs with application to parameter estimation
Infinite depth–width limit	ResNets of All Shapes and Sizes: Quantitative Large-Scale Theory of Training Dynamics
infinitely countable data	Non-Asymptotic Convergence of Discrete Diffusion Models: Masked and Random Walk dynamics
Inhomogeneous Poisson process	Bayesian nonparametric inference for covariate-driven point processes
Inhomogeneous random graphs	The spectrum of dense kernel-based random graphs
Inhomogeneous subordination	Additive subordination of multiparameter Markov processes
Integrable probability	Stationary half-space random growth, via combinatorics
Integral Probability Metrics	Two-sample test for laws of random probabilities via optimal transport
Inter-annotator metric	Modeling Vagueness in Large Language Models: A Hybrid Logical-Probabilistic Perspective on Moral Classification and Constrained Generation
interacting particle system	Massive Particle Systems, Wasserstein Brownian Motions, and the Dean--Kawasaki SPDE PDEs driven by Dirichlet-Ferguson laplacian in Wasserstein-Sobolev spaces
Interacting particle systems	A multiscale analysis of mean-field transformers in the moderate interaction regime Non-chaotic interacting particle systems Nonparametric Estimation of the Diffusive Interaction Function in Particle Systems Critical density of the Stochastic Sandpile Model McKean–Vlasov dynamics with killing and memory: probabilistic representations of a McKean-type PDE Fluctuations of the Simple Exclusion Process on Point Processes Well-posedness of a stochastic reacting particle system with non-local and Lennard–Jones interactions Statistical inference for interacting particle systems driven by the fractional Brownian motion Intermediate Interactions in Particle Systems: Applications to Fluid Dynamics and Biological Modeling Contact process on interchange process Deep Transformers as Mean-field Interacting Particle Systems
Interacting particles	Stochastic McKean-Vlasov dynamics with singular Lennard-Jones drift: a mesoscale regularization
Interacting urns	Urn models: interaction, synchronization and generalized reinforcement
Interaction modelling	Computationally efficient hierarchical additive interaction models through hierarchical ANOVA kernels and Gaussian processes
Interlacing	Well-posedness of a stochastic reacting particle system with non-local and Lennard–Jones interactions
Intermediate Interaction	Intermediate Interactions in Particle Systems: Applications to Fluid Dynamics and Biological Modeling
Interval distance	An Application of Fuzzy Set Theory and Interval-Based Distances for Expert Judgment Aggregation
Intrinsic stochasticity	Intrinsic stochasticity in the Landau–Lifshitz–Navier–Stokes equations on logarithmic lattices
Invariant and ergodic measures	On the uniqueness of reversible invariant measures for SPDEs on the full space
Invariant measure	Linearization of McKean SDEs with application to parameter estimation Exponential integrability of the solution and the invariant measure to the stochastic Burgers equation
Invariant Measures	Existence, uniqueness and asymptotic stability of invariant measures for the stochastic Allen–Cahn–Navier–Stokes system with singular potential Invariant measures for one-dimensional stochastic compressible fluid equations Invariant measures for the open KPZ equation
Inverse problem	Approximation of first passage times and hitting times for stochastic differential equations
Inverse Problems	Low-Dose Tomography of Random Fields and the Problem of Continuous Heterogeneity
inviscid limit	Intrinsic stochasticity in the Landau–Lifshitz–Navier–Stokes equations on logarithmic lattices
Irreducibility	Strong Feller property and irreducibility for stochastic PDEs with degenerate multiplicative noise
Irregular Data	A Risk Minimization Approach to PCA with Irregular Data
Isospectrality	Can one hear the shape of a random matrix?
Ito–Stokes Drift	Averaging Dynamics and Wong-Zakai approximations for a Fast-Slow Navier-Stokes System Driven by fractional Brownian Motion
Itô formula	Wick integrals
J
Jackson Queueing Networks	Stability and renormalization of Jackson networks with non-idling mobile servers
Jumps	A Double Jump Stochastic Volatility model based on a Compound CARMA(p,q)-Hawkes
Jump–diffusion processes	Robust Ergodic Singular Control of Compound–Poisson Jump Diffusions under Drift and Intensity Ambiguity
K
k-statistics	Efficient computation and estimation of generalized cumulants via complementary set partitions
Kasteleyn theory	The bead model and the macroscopic behaviour of Gelfand-Tsetlin patterns
Kernel	Computationally efficient hierarchical additive interaction models through hierarchical ANOVA kernels and Gaussian processes
kernel methods	Approximate Bayesian computation with kernel Wasserstein distance Kernel Quantile Embeddings and Associated Probability Metrics
Kilbas-Saigo function	Non-local operators for Pearson diffusions
Kinetic constraints	Scaling limits of the one-dimensional facilitated exclusion process
Kinetic dynamics	Strong regularisation-by-noise for degenerate SDEs of kinetic type: results and open problems
Knock-out tournaments	Play longer when It matters: optimal match length in knock-out tournaments
Knowledge distillation	Learning from Surrogate Data: Weak-to-Strong Generalization through the Lens of High-Dimensional Regression
Kolmogorov equations	Kolmogorov equations for stochastic Volterra processes with singular kernels Pathwise uniqueness by noise for stochastic PDEs with singular drift Chapter 2: Transport Equation and Kolmogorov equations
Koopman operators	Learning ergodic dynamical systems from finite trajectories
KPZ	Invariant measures for the open KPZ equation
Kraichnan model	Anomalous phenomena in the Kraichnan model of turbulence Chapter 4: The nonsmooth Kraichnan model
Kronecker products	Computationally efficient hierarchical additive interaction models through hierarchical ANOVA kernels and Gaussian processes
Krylov	Low-Dose Tomography of Random Fields and the Problem of Continuous Heterogeneity
Kullback-Leibler Divergence	An Analogue Fr\'echet-Shohat Moments Convergence Theorem for Indeterminate Moment Problems
L
L\'evy processes	Thorin processes: subordination and applications
label noise	Conformal classification with tight marginal coverage in noisy settings
Labeled datasets	Flowing Datasets with Wasserstein over Wasserstein Gradient Flows
Large deviation principles	(Moment) Lyapunov stability of parabolic SPDEs
Large deviations	Laplace's first law of errors applied to Markov and non-Markov diffusive motion Probability graphons and large deviations for random weighted graphs Estimate of the exit time for the Long Range Ising model on random regular graphs Beyond NNGP: Large Deviations and Feature Learning in Bayesian Neural Networks Exponential Random Edge-Colored Graphs via Probability Graphons: Free Energies and Extremal Colorings Large deviations for spatial coagulation with diffusion Large deviations for stochastic approximation: A weak convergence approach
Large Deviations Principle	Zero-noise selection and Large Deviations in $L^\infty_t L^p_x$ for the stochastic transport equation beyond DiPerna-Lions
large financial market	Real-world models for multiple term structures: a unifying HJM semimartingale framework
Large Language Models	Modeling Vagueness in Large Language Models: A Hybrid Logical-Probabilistic Perspective on Moral Classification and Constrained Generation
Large-sample asymptotics	Large-sample asymptotics of coalescent importance sampling algorithms
last passage percolation	Stationary half-space random growth, via combinatorics
Lazy Training	Quantitative Convergence of Trained Quantum Neural Networks to a Gaussian Process
Learning Theory	Algorithm- and Data-Dependent Generalization Bounds for Diffusion Models
Least Concave Majorant	Inference for a concave distribution function under measurement error
Lennard--Jones potential	Well-posedness of a stochastic reacting particle system with non-local and Lennard–Jones interactions
Lennard-Jones potential	Stochastic McKean-Vlasov dynamics with singular Lennard-Jones drift: a mesoscale regularization
Levy processes	Non-selection of Lagrangian trajectories in the zero-noise limit
Levy-type processes	Two-factor models via subordination of multiparameter Markov processes
Lightning Network	Payment-failure times for random Lightning paths
Likelihood approximation	Guidelines for Cubature-based Likelihood approximation of 3D Poisson Point Processes
Limit theorems	Edgeworth Expansions and Non-Gaussian Corrections in Finite-Width Wide Neural Networks A multi-factorial innovation model with feature-interaction Limit theorems for functionals of stationary Gaussian fields
Limiting spectral distribution	Can one hear the shape of a random matrix?
Linear models	Wasserstein Least Squares: statistics, geometry, and algorithms
linear rough-stochastic equations	Malliavin Calculus for rough stochastic differential equations
Local Volatility	Parametric local volatility: Exact prices lead to sound continuous Markovian models
log-periodic perturbation	Generalized Fractional Derivative Operators and Fractional Diffusion Equations Connected to Semistable Lévy Processes
logarithmic lattice	Intrinsic stochasticity in the Landau–Lifshitz–Navier–Stokes equations on logarithmic lattices
Logarithmic Sobolev inequality	Hypercontractivity type property for generalized Mehler semigroups
logistic branching process	Multi-type logistic branching processes with selection: frequency process and genealogy for large carrying capacities
Lognormal diffusion processes	Capturing Growth and Shock Dynamics through Lognormal Diffusions with Binomial Catastrophes
Long Memory	Fractional Cointegration of Geometric Functionals
Long-range dependence	Limit theorems for space-time Gaussian fields on $\mathbb R^d$
long-range Ising model	Estimate of the exit time for the Long Range Ising model on random regular graphs
longest increasing subsequence problem	Stationary half-space random growth, via combinatorics
Lookdowns	Dice processes, moment duality, and the propagation of exchangeability
Lorentz process	Random Flights and Anomalous Diffusion: A non-Markovian Take on Lorentz Processes
Lotteries	Ordering and measuring the complexity of lotteries
Low intensity	A jewel and two dials in the ideal Poisson--Voronoi tessellation
LQ mean-field control	Mean-field control of heterogeneous systems
Lyapunov criterion	Noise induced stabilization in stochastic chemical reaction network
Lyapunov exponent	On the Lyapunov exponent of discrete and continuum generalized Ising-models
Lyapunov exponents	A mild rough Gronwall lemma with applications to non-autonomous evolution equations
Lyapunov Function	Stability and renormalization of Jackson networks with non-idling mobile servers
Lyapunov functions	On Forgetting and Stability of Score-based Generative models
Lyapunov stability	(Moment) Lyapunov stability of parabolic SPDEs
Lévy measures	Fractional Calculus and Gaussian Processes: extensions and alternatives to fractional Brownian motion
Lévy processes hitting times	Lévy processes as weak limits of rough Heston models
Lévy-type processes	Additive subordination of multiparameter Markov processes
M
Machine Learning	Modeling Vagueness in Large Language Models: A Hybrid Logical-Probabilistic Perspective on Moral Classification and Constrained Generation Normalizing Flows as Approximations of the Optimal Transport Map The Volterra signature
Magnetohydrodynamics	Background {Vlasov} equations and {Young} measures for passive scalar and vector advection equations under special stochastic scaling limits
Majorization	Extreme value statistics for partial orders
Malliavin calculus	Malliavin Calculus for rough stochastic differential equations
Malliavin regularity	Limit theorems for functionals of stationary Gaussian fields
Manifold Denoising	Score-based fields on manifolds for denoising
manifold learning	Adaptive denoising diffusion modelling via random time reversal
marginal validity	Conformal classification with tight marginal coverage in noisy settings
Markov bases	Exploring the space of graphs with fixed discrete curvatures
Markov chain Monte Carlo	Bayesian nonparametric inference for covariate-driven point processes
Markov chain Monte Carlo algorithms	Exploring the space of graphs with fixed discrete curvatures
Markov chains	Payment-failure times for random Lightning paths
Markov process \and	Efficient simulation of a new class of Volterra-type SDEs
Markov processes	Additive subordination of multiparameter Markov processes Stability and renormalization of Jackson networks with non-idling mobile servers Learning ergodic dynamical systems from finite trajectories
Markov selections	Chapter 1: Ergodicity and Markov Selections
Markovian lift	Kolmogorov equations for stochastic Volterra processes with singular kernels
Markovian Projection	Exponential Convergence Guarantees for Iterative Markovian Fitting
Martin-Siggia-Rose formalism	Stochastic Differential Equations and the Martin-Siggia-Rose Formalism: An Algebraic-Analytic Correspondence
Martingale Problem	Martingale Problems with Distributional Drift via Regularisation: Convergence of the Euler Scheme
masked diffusion	Non-Asymptotic Convergence of Discrete Diffusion Models: Masked and Random Walk dynamics
Master equations	Master Equations for Continuous-Time Random Walks with Stochastic Resetting
mathematical finance	Invariant cones for jump-diffusions in infinite dimensions
max-flow min-cut theorem	The geometry of the stability region of randomly modulated queuing systems
Maximal regularity	Chapter 3: Scaling limits and delayed blow-up by transport noise
maximality principle	Optimal resource extraction with a random threshold
Maximum Entropy	An Analogue Fr\'echet-Shohat Moments Convergence Theorem for Indeterminate Moment Problems
Maximum likelihood estimation	Capturing Growth and Shock Dynamics through Lognormal Diffusions with Binomial Catastrophes
Maximum principle	A Novel Approach to Peng's Maximum Principle for McKean-Vlasov Stochastic Differential Equations
McKean SDEs with distributional coefficients	A non-local singular McKean SDE
McKean-Vlasov	Linearization of McKean SDEs with application to parameter estimation Mean field optimal stopping and related N -player cooperative games A stochastic approach to time-dependent BEC
McKean-Vlasov equation	A Novel Approach to Peng's Maximum Principle for McKean-Vlasov Stochastic Differential Equations
McKean-Vlasov equations	Nonlinear Rough Fokker-Planck Equations Numerical Approximation of McKean-Vlasov SDEs via Stochastic Gradient Descent
McKean-Vlasov optimal control	Optimal control of McKean-Vlasov systems under partial observation and hidden Markov switching
McKean-Vlasov-type nonlinear SDEs	McKean–Vlasov dynamics with killing and memory: probabilistic representations of a McKean-type PDE
mean field control	Singular Mean-field Control via Singular Mean-field Games Convergence for linear quadratic potential mean field games
Mean field game	Environmental asset, Optimal control, N-players game, Social Planner, Pigouvian tax, Mean field game
mean field games	Stationary Mean Field Games on networks with sticky transition condition Singular Mean-field Control via Singular Mean-field Games A probabilistic approach for optimal stopping mean-field games Mean field games in Hilbert spaces Convergence for linear quadratic potential mean field games Mean field games with option to buy information Uniqueness for Finite-State Mean Field Games with Non-Separable Hamiltonians
Mean field optimal stopping	Mean field optimal stopping and related N -player cooperative games
mean-field	A stochastic volatility approximation for a tick-by-tick price model with mean-field interaction Intermediate Interactions in Particle Systems: Applications to Fluid Dynamics and Biological Modeling Deep Transformers as Mean-field Interacting Particle Systems
Mean-field approximation	Stochastic McKean-Vlasov dynamics with singular Lennard-Jones drift: a mesoscale regularization
Mean-field control	Mean-field control of heterogeneous systems Mean-Field Optimal Control Approach to Deep Learning
mean-field control problems	Stationary Mean-Field singular control of an Ornstein-Uhlenbeck process
Mean-field equation	A Novel Approach to Peng's Maximum Principle for McKean-Vlasov Stochastic Differential Equations
mean-field games	Relative Performance Concerns in Financial Markets under Recursive Intertemporal Preferences Stationary Mean-Field singular control of an Ornstein-Uhlenbeck process Existence of Strong Randomized Equilibria in Mean-Field Games of Optimal Stopping with Common Noise Mean-Field Games in Hilbert Spaces: A Viscosity Approach Fast-slow mean-field games with common noise
Mean-field limit	A multiscale analysis of mean-field transformers in the moderate interaction regime ResNets of All Shapes and Sizes: Quantitative Large-Scale Theory of Training Dynamics Mean-field limit in quantum neural networks
Membership functions	Optimizing Fuzzy Partitions for Visual Sensors
Memory effects	{Macro-Micro Inference for Galves-Löcherbach Processes: Robust Synaptic Classification via Spike-Triggered Extrapolation
Mesoscale	Stochastic McKean-Vlasov dynamics with singular Lennard-Jones drift: a mesoscale regularization
Metastability	The grass-bushes-trees process on a scale-free network Estimate of the exit time for the Long Range Ising model on random regular graphs Metastability of Glauber dynamics with inhomogeneous coupling disorder
Metric graphs	Sticky vertices with energy accumulation
mild Gronwall lemma	A mild rough Gronwall lemma with applications to non-autonomous evolution equations
Mild solutions	Stochastic Evolution Inclusions with Nonlocal Initial Conditions
min-max martingale measures	Does cooperation improve individual performance?
MinHashing	Maintaining k-MinHash Signatures over Fully-Dynamic Data Streams with Recovery
minimum volume	Conditional Coverage in Conformal Prediction: Tradeoffs and Insights
Minkowski sum	The geometry of the stability region of randomly modulated queuing systems
Mixed outcomes	Permutation Tests and NPC Methodology. Theory and Application in Education, in Clinical Research and in Social Security
Mixing	Accurate Bayesian inference for tail risk extrapolation in time series
mixing time	Mixing trichotomy for random walks on directed stochastic block models
Modeling Principles	Separate Exchangeability as Modeling Principle in Bayesian Nonparametrics
Modified log-Sob	Modified logarithmic Sobolev inequalities for point processes
Momen duality	Dice processes, moment duality, and the propagation of exchangeability
moment problem	The moment problem beyond finite dimensions
Moments	Correlation Structure for Random Waves
Monkeypox virus	Modeling Monkeypox transmission through stochastic dynamics with self-excitation
Monte Carlo sampling	Multivariate additive subordination with applications in finance
Moral Value Detection	Modeling Vagueness in Large Language Models: A Hybrid Logical-Probabilistic Perspective on Moral Classification and Constrained Generation
mortal random walker	Target hitting counting process in networks and applications to evanescent random walks
Motions in higher space	Multidimensional random motions with a natural number of velocities
Multi-Criteria Decision-Making	Multi-Criteria Decision-Making, Conditional Probabilities, and Fuzzy Sets
Multi-Criteria Group Decision-Making	Artificial Experts in Multi-Criteria Group Decision-Making
Multi-index model	LEARNING THEORY OF SHALLOW NEURAL NETWORKS THROUGH THE LENS OF RKBS
Multi-scale	Fast-slow mean-field games with common noise
Multidrawing	Urn models: interaction, synchronization and generalized reinforcement
multifractality	A stochastic volatility approximation for a tick-by-tick price model with mean-field interaction
multilayer networks	Simultaneous global and local clustering in multiplex networks with covariate information
Multilevel model	Hierarchical Random Measures without Tables
Multiparameter Markov processes	Two-factor models via subordination of multiparameter Markov processes
Multiparameter stochastic processes	Additive subordination of multiparameter Markov processes
Multiple Agents	Collective Arbitrage and Superreplication
Multiple Comparisons	Distribution-Free Outlier Detection and Enumeration
Multiple networks	Nested stochastic block model for simultaneously clustering networks and nodes
Multiple partition models	Dynamic network clustering via connectivity pattern persistence and node-level dependence
Multiplicative noise	The nonlinear Schrödinger equation with multiplicative noise and arbitrary power of the nonlinearity
multiscale analysis	A multiscale analysis of mean-field transformers in the moderate interaction regime
Multitype contact process	The grass-bushes-trees process on a scale-free network
Multivariate additive subordination	Multivariate tempered stable additive subordination for financial models
Multivariate asset modeling	Multivariate tempered stable additive subordination for financial models
multivariate binomial process	An EWMA Control Chart to Monitor a Multivariate Binomial Process
Multivariate Inference	Permutation Tests and NPC Methodology. Theory and Application in Education, in Clinical Research and in Social Security
Multivariate regular variation	Testing for Multivariate Regular Variation
Multivariate risk measures	Multivariate Robust Extremiles
Multivariate stochastic processes	Multivariate additive subordination with applications in finance
N
N -player cooperative games	Mean field optimal stopping and related N -player cooperative games
N-players game	Environmental asset, Optimal control, N-players game, Social Planner, Pigouvian tax, Mean field game
Natural Language Processing	Modeling Vagueness in Large Language Models: A Hybrid Logical-Probabilistic Perspective on Moral Classification and Constrained Generation
Navier-Stokes Equations	Averaging Dynamics and Wong-Zakai approximations for a Fast-Slow Navier-Stokes System Driven by fractional Brownian Motion
Nelson stochastic mechanics	A stochastic approach to time-dependent BEC
Nested Dirichlet process	Nested stochastic block model for simultaneously clustering networks and nodes
network	The critical percolation window in growing random graphs Bayesian Nonparametric Community Detection in Stochastic Block Models with Structural Constraints
network geometry	Localized geometry detection in scale-free random graphs
networks	Stationary Mean Field Games on networks with sticky transition condition Economic growth models on networks with regime-switching dynamics
Neural networks	Edgeworth Expansions and Non-Gaussian Corrections in Finite-Width Wide Neural Networks Learning with Neural Networks on Structured Inputs Non-universal fluctuations for functionals of random neural networks Quantitative Master Theorems for Tensor Programs via the Wasserstein distance LEARNING THEORY OF SHALLOW NEURAL NETWORKS THROUGH THE LENS OF RKBS
Neural SPDEs	Modeling with neural SPDEs: data-driven Heath-Jarrow-Morton models
Neuro-behavioral data integration	Cognitive data analysis with Bayesian Drift Diffusion Model
Nodal volume	New Chaos Decomposition of Gaussian Nodal Volumes
Nodal volume fluctuations	Statistics on Yau's conjecture
Node Immunization	Node immunization via random forests
node2vec random walks	node2vec random walks: Regular graphs and recurrence
Noise sensitivity	Noise sensitivity and directed polymers
non-asymptotic convergence	Non-Asymptotic Convergence of Discrete Diffusion Models: Masked and Random Walk dynamics
Non-commutative probability	The forward-backward approach to interacting fermionic states on the lattice
Non-convex Optimization	Global Optimization via Softmin Energy Minimization
Non-homogeneous Poisson process	Multidimensional random motions with a natural number of velocities
Non-Homogeneous Random Graphs	Finite vs Infinite-Mean Heavy-Tailed Fitness: Geometry and Connectivity in Inhomogeneous Random Graphs
Non-Kolmogorovian Probability	A Quantum-Probabilistic Framework for Decision-Making under Vagueness
Non-linear PDEs	Non-chaotic interacting particle systems
non-linearity	A stochastic volatility approximation for a tick-by-tick price model with mean-field interaction
non-local dynamics	On some stochastic models of Anomalous Diffusion
Non-local operators	Generalizations of Elastic Brownian Motion Sticky vertices with energy accumulation
non-monotonicity	Event Valence and Subjective Probability
Non-separable Hamiltonians	Uniqueness for Finite-State Mean Field Games with Non-Separable Hamiltonians
Nonlinear associations	Nonparametric Inference for Multivariate and Complex Data Structures
Nonlinear reaction-diffusion PDEs	McKean–Vlasov dynamics with killing and memory: probabilistic representations of a McKean-type PDE
nonlinear SDEs	Numerical Approximation of McKean-Vlasov SDEs via Stochastic Gradient Descent
Nonlocal size bias of order α	Nonlocal α-size biasing: Stein characterization and one-sided concentration bound
Nonparametric Combination	Permutation Tests and NPC Methodology. Theory and Application in Education, in Clinical Research and in Social Security
Nonparametric Empirical Bayes	Score-based fields on manifolds for denoising
nonparametric models	Posterior behaviour of the stick-breaking weights for Bayesian infinte mixture models
Nonparametric test	Inference for a concave distribution function under measurement error
Normalizing Flows	Normalizing Flows as Approximations of the Optimal Transport Map
Nothing else	Modified logarithmic Sobolev inequalities for point processes
Numerical Approximation	Martingale Problems with Distributional Drift via Regularisation: Convergence of the Euler Scheme
Nusselt number	Transport noise in natural convection
O
ODE with discontinuities	Stability and renormalization of Jackson networks with non-idling mobile servers
Operator learning	Deep Hilbert Galerkin methods for PDEs on Hilbert spaces via derivative-informed operator learning with applications to stochastic optimal control of infinite-dimensional systems Derivative-informed Hilbert neural operators solve PDEs on Hilbert spaces and infinite-dimensional optimal control problems
Operator semigroups	Random evolution on combinatorial and metric graphs
Opinion Dynamics	Reduced stochastic PDE models for collective behaviour
Optimal annuitization	Optimal Annuitization under Partially Observable Mortality
Optimal autonomous trading strategies	Optimal autonomous trading strategies in models based on Ornstein-Uhlenbeck processes with mean-reverting levels
optimal control	Environmental asset, Optimal control, N-players game, Social Planner, Pigouvian tax, Mean field game Fast-slow mean-field games with common noise
Optimal double-stopping problem	Optimal autonomous trading strategies in models based on Ornstein-Uhlenbeck processes with mean-reverting levels
Optimal match-length	Play longer when It matters: optimal match length in knock-out tournaments
Optimal stochastic control	Continuous-Time Dynamic Contracting With Limited Commitment
Optimal stopping	The Wiener Disorder Problem with Random Post-Disorder Drift Optimal Annuitization under Partially Observable Mortality A probabilistic approach for optimal stopping mean-field games Continuous-Time Dynamic Contracting With Limited Commitment Existence of Strong Randomized Equilibria in Mean-Field Games of Optimal Stopping with Common Noise Fast-slow mean-field games with common noise
Optimal transport	An optimal transport foundation for a class of dynamically consistent risk measures Flowing Datasets with Wasserstein over Wasserstein Gradient Flows Two-sample test for laws of random probabilities via optimal transport Normalizing Flows as Approximations of the Optimal Transport Map Wasserstein Least Squares: statistics, geometry, and algorithms
Optimization Dynamics	Algorithm- and Data-Dependent Generalization Bounds for Diffusion Models
Option pricing	Multivariate additive subordination with applications in finance
Ordinal covariance	Some results on general $\Lambda$-quantiles
Orstein-Uhlenbeck process	On some drift-based transformations of multidimensional diffusion processes and their applications
Orthogonal polynomials	Statistical inference for SDEs using Signatures
P
Palm calculus	Association in Spatial Queueing-Filtering Networks
Parabolic-type free-boundary problem	Optimal autonomous trading strategies in models based on Ornstein-Uhlenbeck processes with mean-reverting levels
Partial differential equations	Multidimensional random motions with a natural number of velocities
Partial differential equations on spaces of probability measures	PDEs driven by Dirichlet-Ferguson laplacian in Wasserstein-Sobolev spaces
Partial exchangeability	Separate Exchangeability as Modeling Principle in Bayesian Nonparametrics Hierarchical Random Measures without Tables
Partial information	Optimal Annuitization under Partially Observable Mortality Optimal reinsurance with unobservable claim arrival intensity: a Stackelberg differential game
partial observation	Optimal control of McKean-Vlasov systems under partial observation and hidden Markov switching
Particle Swarm	Global Optimization via Softmin Energy Minimization
Partition optimization	Optimizing Fuzzy Partitions for Visual Sensors
Passive Scalars	Background {Vlasov} equations and {Young} measures for passive scalar and vector advection equations under special stochastic scaling limits
Pathwise uniqueness by noise	Pathwise uniqueness by noise for stochastic PDEs with singular drift
PDEs in Infinite Dimensional Spaces	Mean-Field Games in Hilbert Spaces: A Viscosity Approach
Pearson diffusion	Non-local operators for Pearson diffusions
percolation	The critical percolation window in growing random graphs Solidification estimates for random walks on supercritical percolation clusters
Periodic solutions	Stochastic Evolution Inclusions with Nonlocal Initial Conditions
Permutation tests	Permutation Tests and NPC Methodology. Theory and Application in Education, in Clinical Research and in Social Security
Phase transition	The critical percolation window in growing random graphs Pinning polymer model in correlated random environment
Pigouvian tax	Environmental asset, Optimal control, N-players game, Social Planner, Pigouvian tax, Mean field game
Plane tree	Can one hear the shape of a random matrix?
Point processes	Long-time behaviour for birth-and-death dynamics in the continuum Functional marked self-exciting point process models A fractional Hawkes process Bayesian calculus and predictive characterizations of extended feature allocation models Modified logarithmic Sobolev inequalities for point processes Large deviations for spatial coagulation with diffusion Random scars : overview and recent advances
Poisson process	On the Markov modulated Poisson process and its application in shock models
Polymer model	Pinning polymer model in correlated random environment
Polymers	Hookean dumbbell model for polymers, stretching noise and turbulence
polynomial approximation	Numerical Approximation of McKean-Vlasov SDEs via Stochastic Gradient Descent
polynuclear growth	Stationary half-space random growth, via combinatorics
portfolio choice	On consistency of optimal portfolio choice for state-dependent exponential utilities
portfolio choice under recursive utility	Relative Performance Concerns in Financial Markets under Recursive Intertemporal Preferences
position-aware generalized Chinese restaurant process	Exchangeable random permutations with an application to Bayesian graph matching
Positive recurrence	Stability of Reaction Networks with Randomly Switching Parameters - Part 1
Posterior concentration	Bayesian nonparametric estimation of spatio-temporal Hawkes processes
Posterior contraction rates	Bayesian nonparametric inference for covariate-driven point processes
Powers of a Hamilton cycle	Sharp thresholds for higher powers of Hamilton cycles in random graphs
Predictive distribution	Asymptotic and empirical properties of some classes of predictive distribution
Predictive distributions	Exchangeable measure-valued Pólya sequences
Predictive inference	Predictive Bernstein-von Mises Theorems
Predictive resampling	Asymptotic and empirical properties of some classes of predictive distribution
Preferential attachment	Diameters in preferential attachment model with random initial degrees
Preferential attachment with random initial degree	Do random initial degrees suppress concentration in preferential attachment graphs?
Principal Components Analysis	A Risk Minimization Approach to PCA with Irregular Data
Principal-agent models	Continuous-Time Dynamic Contracting With Limited Commitment
Probabilistic Analysis of Algorithms	Maintaining k-MinHash Signatures over Fully-Dynamic Data Streams with Recovery
Probabilistic Data Structure and Algorithms	Maintaining k-MinHash Signatures over Fully-Dynamic Data Streams with Recovery
Probabilistic representation	A non-local singular McKean SDE
Probability	Stability of Reaction Networks with Randomly Switching Parameters - part 2
Probability graphons	Probability graphons and large deviations for random weighted graphs Exponential Random Edge-Colored Graphs via Probability Graphons: Free Energies and Extremal Colorings
process	Boltzmann processes
product form	Large-Scale Analysis of Multi-Scale Queuing Networks: Applications to Car-Sharing Systems
projective limit	The moment problem beyond finite dimensions
Projective processes	(Moment) Lyapunov stability of parabolic SPDEs
Prokhorov’s condition	The moment problem beyond finite dimensions
Propagation of chaos	Non-chaotic interacting particle systems Mean-field limit in quantum neural networks
Proper conditional distributions	Exchangeable measure-valued Pólya sequences
Pure Jumps	Parametric local volatility: Exact prices lead to sound continuous Markovian models
Pyramid Extrapolation	{Macro-Micro Inference for Galves-Löcherbach Processes: Robust Synaptic Classification via Spike-Triggered Extrapolation
Pólya urns	Exchangeable measure-valued Pólya sequences
Q
Quantiles	Some results on general $\Lambda$-quantiles Multivariate Robust Extremiles
Quantum Cognition	A Quantum-Probabilistic Framework for Decision-Making under Vagueness
Quantum dynamics	Random scars : overview and recent advances
Quantum graphs	Random evolution on combinatorial and metric graphs
Quantum Markov Semigroups	Some structural results for Gaussian Quantum Markov Semigroups
Quantum Neural Networks	Quantitative Convergence of Trained Quantum Neural Networks to a Gaussian Process Mean-field limit in quantum neural networks
Quantum Resource Theories	Extreme value statistics for partial orders
quasi-Bayes	Dimension-free statistical guarantees for fine-tuning of conditional diffusion models via PAC-Bayes bounds
Quasi-convex	Robust quasi-convex and cash-subadditive risk measures: theory, duality, and applications
Queueing theory	Association in Spatial Queueing-Filtering Networks
queuing networks	Large-Scale Analysis of Multi-Scale Queuing Networks: Applications to Car-Sharing Systems
queuing systems	The geometry of the stability region of randomly modulated queuing systems
R
Radon Transform	Low-Dose Tomography of Random Fields and the Problem of Continuous Heterogeneity
random digraphs	Mixing trichotomy for random walks on directed stochastic block models
Random drift	The Wiener Disorder Problem with Random Post-Disorder Drift
random dynamical systems	Random Quadratic Form on a Sphere: Synchronization by Common Noise
Random environment	Hard wall repulsion for the discrete Gaussian free field in random environment in supercritical dimension Fluctuations of the Simple Exclusion Process on Point Processes
Random feature ridge regression	Learning from Surrogate Data: Weak-to-Strong Generalization through the Lens of High-Dimensional Regression
Random Field	Correlation Structure for Random Waves
random fields	New Chaos Decomposition of Gaussian Nodal Volumes On the Lyapunov exponent of discrete and continuum generalized Ising-models Critical Points and Euler characteristic for Time-Dependent Spherical Random Fields
Random Forests	Node immunization via random forests
random geometry	Spectral and Geometric Phase Transitions in Deep Neural Networks
Random graph	Diameters in preferential attachment model with random initial degrees
random graphs	Sharp thresholds for higher powers of Hamilton cycles in random graphs Competing growth on the configuration model via first-passage percolation and long-range jumps Convergence of subgraph densities in ERGMs Spectral properties of directed inhomogeneous graphs Hydrodynamic limits of exploration processes on large random graphs
Random matrices	Spectral properties of directed inhomogeneous graphs The spectrum of dense kernel-based random graphs
Random matrix	Can one hear the shape of a random matrix?
Random measures	The Wasserstein geometry of random measures
random modulations	The geometry of the stability region of randomly modulated queuing systems
Random Partition Model	Separate Exchangeability as Modeling Principle in Bayesian Nonparametrics
Random Probability Measures	Hilbert-Based Correlation Indices for Distributional Data
random regular graph	Estimate of the exit time for the Long Range Ising model on random regular graphs
Random structures	Diameters in preferential attachment model with random initial degrees
random walk	Non-Asymptotic Convergence of Discrete Diffusion Models: Masked and Random Walk dynamics Solidification estimates for random walks on supercritical percolation clusters
random walks	Mixing trichotomy for random walks on directed stochastic block models
Random waves	Berry-Heisenberg random waves
Random weighted graphs	Probability graphons and large deviations for random weighted graphs Exponential Random Edge-Colored Graphs via Probability Graphons: Free Energies and Extremal Colorings
Randomized Algorithms	Threshold-Driven Streaming Graph: Expansion and Rumor Spreading The Minority Dynamics
Rank Tests	Distribution-Free Outlier Detection and Enumeration
Ranked data	Nonparametric Inference for Multivariate and Complex Data Structures
reaction network	Stochastic ordering tools for reaction network models
Reactions Networks	Stability of Reaction Networks with Randomly Switching Parameters - part 2
Rearranged stochastic heat equation	Entropic Regularization of Rearranged Stochastic Heat Equation
Recursive algorithms	Large deviations for stochastic approximation: A weak convergence approach
reflected BSDEs	A probabilistic approach for optimal stopping mean-field games
regime-switching	Economic growth models on networks with regime-switching dynamics
Regression	Wasserstein Least Squares: statistics, geometry, and algorithms
Regular graphs	node2vec random walks: Regular graphs and recurrence
regularity structures	Large field problem in coercive singular PDEs
Regularization by noise	The nonlinear Schrödinger equation with multiplicative noise and arbitrary power of the nonlinearity Chapter 3: Scaling limits and delayed blow-up by transport noise Non-selection of Lagrangian trajectories in the zero-noise limit Refined uniqueness results for 2D Euler and gSQG with rough Kraichnan noise Chapter 4: The nonsmooth Kraichnan model
Regularly varying time series	Self-normalization of sums of dependent random variables
Reinforced processes	Urn models: interaction, synchronization and generalized reinforcement
Reinforced random walk	Interacting vertex reinforced random walks on complete subgraphs with simultaneous and independent transitions
Reinsurance	Optimal reinsurance with unobservable claim arrival intensity: a Stackelberg differential game
Rejection sampling	Approximation of Diffusion Exit Times from Bounded Domains via a Rejection-Based Random Walk
Relative entropy	Long-time behaviour for birth-and-death dynamics in the continuum
renormalisation group	Flow equation approach to stochastic quantisation
Reproducing kernel Banach spaces	LEARNING THEORY OF SHALLOW NEURAL NETWORKS THROUGH THE LENS OF RKBS
Reproducing Kernel Hilbert Spaces	Hilbert-Based Correlation Indices for Distributional Data
Resampling	Large-sample asymptotics of coalescent importance sampling algorithms
Residual Neural Networks	ResNets of All Shapes and Sizes: Quantitative Large-Scale Theory of Training Dynamics
resource extraction	Optimal resource extraction with a random threshold
Reversible investment	When investors force the green transition: a two-dimensional singular stochastic control problem
reward-guided alignment	Dimension-free statistical guarantees for fine-tuning of conditional diffusion models via PAC-Bayes bounds
Richardson’s law	Anomalous phenomena in the Kraichnan model of turbulence
Riemann–Hilbert problems	Stationary half-space random growth, via combinatorics
Risk	Ordering and measuring the complexity of lotteries
Risk and deviation measures	Integrated expectile-based measures of inequality
risk generator	An optimal transport foundation for a class of dynamically consistent risk measures
Risk meausres	Robust quasi-convex and cash-subadditive risk measures: theory, duality, and applications
Risk neutral density	Functional PCA for Risk-Neutral densities in Bayes space
RKHS	Low-Dose Tomography of Random Fields and the Problem of Continuous Heterogeneity
Robust control	Robust Ergodic Singular Control of Compound–Poisson Jump Diffusions under Drift and Intensity Ambiguity
Robustness	Multivariate Robust Extremiles
Rosenblatt distribution	Limit theorems for space-time Gaussian fields on $\mathbb R^d$
Rosenblatt process	Wick integrals
Rough Analysis	Recent Developments on Singular SPDEs in Heterogeneous Media and Curved Spaces
rough boundary noise	A mild rough Gronwall lemma with applications to non-autonomous evolution equations
rough differential equations	Rough differential equations for volatility
Rough Heston model	Stochastic Volterra Equations on Convex Domains Lévy processes as weak limits of rough Heston models
rough Kraichnan noise	Refined uniqueness results for 2D Euler and gSQG with rough Kraichnan noise
rough partial differential equations	A mild rough Gronwall lemma with applications to non-autonomous evolution equations
rough path theory	Large field problem in coercive singular PDEs
rough paths	Nonlinear Rough Fokker-Planck Equations Rough differential equations for volatility The Volterra signature Malliavin Calculus for rough stochastic differential equations
rough volatility	Kolmogorov equations for stochastic Volterra processes with singular kernels Rough differential equations for volatility
RSK correspondence	Stationary half-space random growth, via combinatorics
Rumor Spreading	Threshold-Driven Streaming Graph: Expansion and Rumor Spreading
S
Sato processes	Multivariate tempered stable additive subordination for financial models
scale-free graphs	Localized geometry detection in scale-free random graphs
Scaling	Stability and renormalization of Jackson networks with non-idling mobile servers
Scaling limit	Hookean dumbbell model for polymers, stretching noise and turbulence
scaling limits	Large-Scale Analysis of Multi-Scale Queuing Networks: Applications to Car-Sharing Systems Deep Transformers as Mean-field Interacting Particle Systems
scaling limits of interacting populations	Multi-type logistic branching processes with selection: frequency process and genealogy for large carrying capacities
scheduling	The geometry of the stability region of randomly modulated queuing systems
Schrödinger Bridge	Exponential Convergence Guarantees for Iterative Markovian Fitting
Schrödinger Bridges	Beyond Schrödinger Bridges for Learning Trajectories from Snapshot Samples
score matching	Adaptive denoising diffusion modelling via random time reversal
score monotonicity	Non-Asymptotic Convergence of Discrete Diffusion Models: Masked and Random Walk dynamics
Score-based Field	Score-based fields on manifolds for denoising
Score-based generative modeling	Theoretical guarantees for diffusion models — beyond log-concavity Sampling error bounds for the denoising diffusion probabilistic model via the Föllmer process
Score-Based Generative Models	On Forgetting and Stability of Score-based Generative models Algorithm- and Data-Dependent Generalization Bounds for Diffusion Models
SDE	Stochastic McKean-Vlasov dynamics with singular Lennard-Jones drift: a mesoscale regularization
Second Quantization	Second Quantization and Evolution Operators in infinite dimension
selection	Gamma duality and a tractable transition density for the Wright-Fisher diffusion with selection
Self-Exciting	A Double Jump Stochastic Volatility model based on a Compound CARMA(p,q)-Hawkes
Self-normalized sums	Self-normalization of sums of dependent random variables
Self-organized criticality	Critical density of the Stochastic Sandpile Model
Self-similar Bernstein functions	Generalized Fractional Derivative Operators and Fractional Diffusion Equations Connected to Semistable Lévy Processes
Semantic Vagueness	A Quantum-Probabilistic Framework for Decision-Making under Vagueness
Semi-fractional derivatives and diffusion equations	Generalized Fractional Derivative Operators and Fractional Diffusion Equations Connected to Semistable Lévy Processes
Semi-Markov processes	On some stochastic models of Anomalous Diffusion
Semiconcavity propagation	A semiconcavity approach to stability of entropic plans and exponential convergence of Sinkhorn's algorithm - Part 2 A semiconcavity approach to stability of entropic plans and exponential convergence of Sinkhorn’s algorithm - Part 1
Semistable Lévy processes	Generalized Fractional Derivative Operators and Fractional Diffusion Equations Connected to Semistable Lévy Processes
SENTINEL-GRID	New Distributed Beacon-Based Approaches for Multi-Parameter Monitoring: Sentinel-GRID
Separate Exchangeability	Separate Exchangeability as Modeling Principle in Bayesian Nonparametrics
Sequential analysis	The Wiener Disorder Problem with Random Post-Disorder Drift
Sequential detection	The Wiener Disorder Problem with Random Post-Disorder Drift
Sequential testing	Play longer when It matters: optimal match length in knock-out tournaments
SGD	Numerical Approximation of McKean-Vlasov SDEs via Stochastic Gradient Descent
Shannon Entropy	An Analogue Fr\'echet-Shohat Moments Convergence Theorem for Indeterminate Moment Problems
Sharp threshold	Sharp thresholds for higher powers of Hamilton cycles in random graphs
Sibuya random variable	Random walks with stochastic resetting in complex networks
Signature method	Statistical inference for SDEs using Signatures
Signatures	The Volterra signature
Signed probabilities	Event Valence and Subjective Probability
Simulation	Efficient Simulation of Affine Volterra Processes Gamma duality and a tractable transition density for the Wright-Fisher diffusion with selection Constructing heavy-tailed directed hypergraphs Parameter estimation in a fractional neuronal model
Sine-Gordon Model	On the Stochastic Sine-Gordon Model from the Viewpoint of Quantum Field Theory
Singular control	Optimal resource extraction with a random threshold When investors force the green transition: a two-dimensional singular stochastic control problem
Singular drift	Well-posedness of a stochastic reacting particle system with non-local and Lennard–Jones interactions
Singular kernels	Stochastic McKean-Vlasov dynamics with singular Lennard-Jones drift: a mesoscale regularization
Singular SDEs	Martingale Problems with Distributional Drift via Regularisation: Convergence of the Euler Scheme
singular stochastic control	Singular Mean-field Control via Singular Mean-field Games Stationary Mean-Field singular control of an Ornstein-Uhlenbeck process
Singular Stochastic Partial Differential Equations	On the Stochastic Sine-Gordon Model from the Viewpoint of Quantum Field Theory
Sinkhorn's algorithm	A semiconcavity approach to stability of entropic plans and exponential convergence of Sinkhorn's algorithm - Part 2
Sinkhorn’s algorithm	A semiconcavity approach to stability of entropic plans and exponential convergence of Sinkhorn’s algorithm - Part 1
SIR dynamics	Infection models on dense dynamic random graphs
Size Bias	Strong disorder for Stochastic Heat Flow and 2D Directed Polymers
Skew	Parametric local volatility: Exact prices lead to sound continuous Markovian models
Skewed distributions	Nonparametric Inference for Multivariate and Complex Data Structures
sliced wasserstein	Kernel Quantile Embeddings and Associated Probability Metrics
Small sample Inference	Permutation Tests and NPC Methodology. Theory and Application in Education, in Clinical Research and in Social Security
Smoluchowski PDE	Large deviations for spatial coagulation with diffusion
social networks	Homophily within and across groups: a maximum-entropy framework for analyzing different social scales
Social Planner	Environmental asset, Optimal control, N-players game, Social Planner, Pigouvian tax, Mean field game
Solidification estimates	Solidification estimates for random walks on supercritical percolation clusters
Sonine pair	Fractional Calculus and Gaussian Processes: extensions and alternatives to fractional Brownian motion
Spatial birth and death	Long-time behaviour for birth-and-death dynamics in the continuum
Spatial random graphs	The spectrum of dense kernel-based random graphs
SPDE	Hookean dumbbell model for polymers, stretching noise and turbulence Invariant measures for the open KPZ equation
SPDEs	Pathwise uniqueness by noise for stochastic PDEs with singular drift Flow equation approach to stochastic quantisation (Moment) Lyapunov stability of parabolic SPDEs Recent Developments on Singular SPDEs in Heterogeneous Media and Curved Spaces
Specialized fuzzifiers	Optimizing Fuzzy Partitions for Visual Sensors
spectra	Spectral properties of directed inhomogeneous graphs
spectral asymptotics	Spectral and Geometric Phase Transitions in Deep Neural Networks
Spectral Gap	On spectral gaps of stochastic wave equations
Spectral representation	Non-local operators for Pearson diffusions
sphere cross time	Critical Points and Euler characteristic for Time-Dependent Spherical Random Fields
Sphere-cross-time Random Fields	Fractional Cointegration of Geometric Functionals
Spike-Triggered Estimator	{Macro-Micro Inference for Galves-Löcherbach Processes: Robust Synaptic Classification via Spike-Triggered Extrapolation
Spreadable processes	On the Ryll-Nardzewski Theorem for Quantum Stochastic Processes
stability	The geometry of the stability region of randomly modulated queuing systems
Stability analysis	On Forgetting and Stability of Score-based Generative models
Stackelberg differential game	Optimal reinsurance with unobservable claim arrival intensity: a Stackelberg differential game
Stackelberg game	Reinsurance games through quantile-constrained Choquet-Wasserstein approximations
standardized residuals	Conditional Coverage in Conformal Prediction: Tradeoffs and Insights
State-dependent killing	Well-posedness of a stochastic reacting particle system with non-local and Lennard–Jones interactions
State-dependent noise	Large deviations for stochastic approximation: A weak convergence approach
state-dependent utility	On consistency of optimal portfolio choice for state-dependent exponential utilities
Stationary distribution	node2vec random walks: Regular graphs and recurrence Stability of Reaction Networks with Randomly Switching Parameters - Part 1
Stationary fields on Lie groups	Berry-Heisenberg random waves
stationary random growth	Stationary half-space random growth, via combinatorics
statistical distances	Kernel Quantile Embeddings and Associated Probability Metrics
Statistical estimates	Parameter estimation in a fractional neuronal model
Statistical inference for stochastic processes	Statistical inference for interacting particle systems driven by the fractional Brownian motion
Statistical learning	LEARNING THEORY OF SHALLOW NEURAL NETWORKS THROUGH THE LENS OF RKBS
Statistical learning theory	Learning ergodic dynamical systems from finite trajectories
Statistical methods for SDEs	Statistical inference for SDEs using Signatures
Stein identity	Nonlocal α-size biasing: Stein characterization and one-sided concentration bound
Stein's Method	Quantitative Convergence of Trained Quantum Neural Networks to a Gaussian Process
sticky transition condition	Stationary Mean Field Games on networks with sticky transition condition
Stieltjes Class	An Analogue Fr\'echet-Shohat Moments Convergence Theorem for Indeterminate Moment Problems
Stochastic Allen-Cahn-Navier-Stokes	Existence, uniqueness and asymptotic stability of invariant measures for the stochastic Allen–Cahn–Navier–Stokes system with singular potential
Stochastic approximation	Interacting vertex reinforced random walks on complete subgraphs with simultaneous and independent transitions Large deviations for stochastic approximation: A weak convergence approach Urn models: interaction, synchronization and generalized reinforcement
Stochastic block model	Bayesian Nonparametric Community Detection in Stochastic Block Models with Structural Constraints Nested stochastic block model for simultaneously clustering networks and nodes
stochastic blockmodel	Simultaneous global and local clustering in multiplex networks with covariate information
Stochastic Burgers equation	Exponential integrability of the solution and the invariant measure to the stochastic Burgers equation
Stochastic calculus of variation	A stochastic approach to time-dependent BEC
stochastic control	Deep Hilbert Galerkin methods for PDEs on Hilbert spaces via derivative-informed operator learning with applications to stochastic optimal control of infinite-dimensional systems Optimal reinsurance with unobservable claim arrival intensity: a Stackelberg differential game Dimension-free statistical guarantees for fine-tuning of conditional diffusion models via PAC-Bayes bounds Derivative-informed Hilbert neural operators solve PDEs on Hilbert spaces and infinite-dimensional optimal control problems
Stochastic differential equations	Strong regularisation-by-noise for degenerate SDEs of kinetic type: results and open problems Stochastic Differential Equations and the Martin-Siggia-Rose Formalism: An Algebraic-Analytic Correspondence
stochastic differential utility	Relative Performance Concerns in Financial Markets under Recursive Intertemporal Preferences
Stochastic Dynamics	Beyond Schrödinger Bridges for Learning Trajectories from Snapshot Samples
Stochastic economic growth model	Economic growth models on networks with regime-switching dynamics
Stochastic epidemic model	Modeling Monkeypox transmission through stochastic dynamics with self-excitation
Stochastic evolution equations	Chapter 2: Transport Equation and Kolmogorov equations
Stochastic evolution inclusions	Stochastic Evolution Inclusions with Nonlocal Initial Conditions
stochastic flows	Stochastic diffuse interface models driven by conservative noise
Stochastic fluid dynamics	Transport noise in natural convection
Stochastic fluids	Invariant measures for one-dimensional stochastic compressible fluid equations
Stochastic geometry	Poisson Hail on a Wireless Ground Association in Spatial Queueing-Filtering Networks
Stochastic gradient descent	Large deviations for stochastic approximation: A weak convergence approach
Stochastic Heat Equation	Strong disorder for Stochastic Heat Flow and 2D Directed Polymers
Stochastic Heat Flow	Strong disorder for Stochastic Heat Flow and 2D Directed Polymers Noise sensitivity and directed polymers
Stochastic Homogenization	Fluctuations of the Simple Exclusion Process on Point Processes
stochastic integral	Wick integrals
stochastic invariance	Invariant cones for jump-diffusions in infinite dimensions
Stochastic localization	Sampling error bounds for the denoising diffusion probabilistic model via the Föllmer process
Stochastic nonlinear Schrödinger equation	The nonlinear Schrödinger equation with multiplicative noise and arbitrary power of the nonlinearity
stochastic optimal control	Optimal Control of Infinite-Dimensional Differential Systems with Randomness and Path-Dependence and Stochastic Path-Dependent Hamilton–Jacobi Equations
Stochastic optimization	Strategic Focus or Technological Neutrality? On the Optimal Mix of Green Investment and Carbon Capture and Storage Research in a Budget-Constraint World ZOBA: An Efficient Single-loop Zeroth-order Bilevel Optimization Algorithm
stochastic ordering	Stochastic ordering tools for reaction network models
Stochastic orderings	First-passage times through closed curves for bivariate diffusion processes, simulations and comparisons based on stochastic orderings
Stochastic orders	Analysis of Systems through the Regression Importance Signature
stochastic partial differential equation	Real-world models for multiple term structures: a unifying HJM semimartingale framework Invariant cones for jump-diffusions in infinite dimensions
Stochastic partial differential equations	Kolmogorov equations for stochastic Volterra processes with singular kernels On the uniqueness of reversible invariant measures for SPDEs on the full space Ergodicity of a Stochastic Energy Balance Model for Global Temperature
Stochastic Particles Methods	Global Optimization via Softmin Energy Minimization
stochastic path-dependent Hamilton-Jacobi equation	Optimal Control of Infinite-Dimensional Differential Systems with Randomness and Path-Dependence and Stochastic Path-Dependent Hamilton–Jacobi Equations
Stochastic PDEs	Chapter 1: Ergodicity and Markov Selections
stochastic processes	Functional marked self-exciting point process models
Stochastic quantisation	Flow equation approach to stochastic quantisation The forward-backward approach to interacting fermionic states on the lattice
Stochastic Reaction Networks	Stability of Reaction Networks with Randomly Switching Parameters - Part 1
Stochastic recursive equations	Constructing heavy-tailed directed hypergraphs
Stochastic resetting	Master Equations for Continuous-Time Random Walks with Stochastic Resetting Random walks with stochastic resetting in complex networks
Stochastic Restart	Generalizations of Elastic Brownian Motion
Stochastic Sandpile Model	Critical density of the Stochastic Sandpile Model
Stochastic transport equation	Zero-noise selection and Large Deviations in $L^\infty_t L^p_x$ for the stochastic transport equation beyond DiPerna-Lions
Stochastic transport equations	Chapter 2: Transport Equation and Kolmogorov equations
Stochastic Volatility	A stochastic volatility approximation for a tick-by-tick price model with mean-field interaction A Double Jump Stochastic Volatility model based on a Compound CARMA(p,q)-Hawkes
Stochastic Volterra Equations	Kolmogorov equations for stochastic Volterra processes with singular kernels Stochastic Volterra Equations on Convex Domains Explosions of stochastic Volterra equations The Volterra signature
Stochastic Wave Equations	On spectral gaps of stochastic wave equations
Stop-loss reinsurance	Reinsurance games through quantile-constrained Choquet-Wasserstein approximations
Stopping time	Measuring Financial Resilience Using Backward Stochastic Differential Equations
Streaming Algorithms	Maintaining k-MinHash Signatures over Fully-Dynamic Data Streams with Recovery
Stretching Noise	Background {Vlasov} equations and {Young} measures for passive scalar and vector advection equations under special stochastic scaling limits
Strong error rate	Efficient simulation of a new class of Volterra-type SDEs
Strong Feller property	Strong Feller property and irreducibility for stochastic PDEs with degenerate multiplicative noise
Strong laws	Interacting vertex reinforced random walks on complete subgraphs with simultaneous and independent transitions
Strong solutions	Well-posedness of a stochastic reacting particle system with non-local and Lennard–Jones interactions
Strong uniqueness	Strong regularisation-by-noise for degenerate SDEs of kinetic type: results and open problems
subgraph densities	Convergence of subgraph densities in ERGMs
subordination	Thorin processes: subordination and applications
Sufficientness postulates	Bayesian calculus and predictive characterizations of extended feature allocation models
Superposition principle	The Wasserstein geometry of random measures
Surface tension	The bead model and the macroscopic behaviour of Gelfand-Tsetlin patterns
survival statistics	Target hitting counting process in networks and applications to evanescent random walks
Symmetric diffusion processes	On some drift-based transformations of multidimensional diffusion processes and their applications
Symmetry	Some structural results for Gaussian Quantum Markov Semigroups
Synaptic inference	{Macro-Micro Inference for Galves-Löcherbach Processes: Robust Synaptic Classification via Spike-Triggered Extrapolation
Synchronization	Random Quadratic Form on a Sphere: Synchronization by Common Noise Urn models: interaction, synchronization and generalized reinforcement
T
Tail algebra	de Finetti theorem for quantum stochastic processes based on twisted products: conditional independence
Tail risk	Accurate Bayesian inference for tail risk extrapolation in time series
Target hitting counting process	Target hitting counting process in networks and applications to evanescent random walks
Telegraph equation	Time-changed random evolutions and fractional hyperbolic-type equations
Telegraph process	Multidimensional random motions with a natural number of velocities
Tensor Programs	Quantitative Master Theorems for Tensor Programs via the Wasserstein distance
TEST1
TEST2
TEST3
Thorin processes	Thorin processes: subordination and applications
Three-dimensional Poisson point processes	Guidelines for Cubature-based Likelihood approximation of 3D Poisson Point Processes
Threshold diffusions	Singular SDEs through interfaces: the threshold Cox-Ingersoll-Ross model
Threshold Exceedances	Accurate Bayesian inference for tail risk extrapolation in time series
Time changes	Non-local dynamic boundary conditions for sticky Brownian motions on smooth domains
time consistency	An optimal transport foundation for a class of dynamically consistent risk measures On consistency of optimal portfolio choice for state-dependent exponential utilities
Time Series	Asymptotic theory for the likelihood-based block maxima method in time series
Time-change	Non-local operators for Pearson diffusions
Time-changed operator	Time-changed random evolutions and fractional hyperbolic-type equations
Time-changed processes	Two-factor models via subordination of multiparameter Markov processes
tipping point	Optimal resource extraction with a random threshold
Total variation distance	Asymptotic and empirical properties of some classes of predictive distribution Edgeworth Expansions and Non-Gaussian Corrections in Finite-Width Wide Neural Networks
Trajectory Inference	Beyond Schrödinger Bridges for Learning Trajectories from Snapshot Samples
transformers	A multiscale analysis of mean-field transformers in the moderate interaction regime Random Quadratic Form on a Sphere: Synchronization by Common Noise
transition function	Gamma duality and a tractable transition density for the Wright-Fisher diffusion with selection
transport equation	A multiscale analysis of mean-field transformers in the moderate interaction regime
Transport map	Properties of diffusion transport maps via creation of log-semiconcavity along heat flows
Transport noise	Averaging Dynamics and Wong-Zakai approximations for a Fast-Slow Navier-Stokes System Driven by fractional Brownian Motion Transport noise in natural convection Chapter 3: Scaling limits and delayed blow-up by transport noise Background {Vlasov} equations and {Young} measures for passive scalar and vector advection equations under special stochastic scaling limits
Transport-stretching noise	Hookean dumbbell model for polymers, stretching noise and turbulence
Trap domains	Non-local dynamic boundary conditions for sticky Brownian motions on smooth domains
Trees	A partial likelihood approach to tree-based density modeling and its application in Bayesian inference
Turbulent transport	Chapter 4: The nonsmooth Kraichnan model
twisted tensor products	On the Ryll-Nardzewski Theorem for Quantum Stochastic Processes
Two-sample test	Two-sample test for laws of random probabilities via optimal transport
U
Uncertainty	Robust quasi-convex and cash-subadditive risk measures: theory, duality, and applications
Uncertainty Quantification	Adaptive variational Gaussian processes A Conformal Prediction Approach to Predict Populations of Graphs
unique ergodicity	Chapter 1: Ergodicity and Markov Selections
Uniqueness of Equilibria	Uniqueness for Finite-State Mean Field Games with Non-Separable Hamiltonians
Unlabelled Graphs	A Conformal Prediction Approach to Predict Populations of Graphs
Urn Models	The Reverse Hypergeometric distribution for attribute concentration in small groups
V
valence	Event Valence and Subjective Probability
vanishing noise	Intrinsic stochasticity in the Landau–Lifshitz–Navier–Stokes equations on logarithmic lattices
variational Bayesian inference	Simultaneous global and local clustering in multiplex networks with covariate information
Variational inference	Adaptive variational Gaussian processes Bayesian nonparametric estimation of spatio-temporal Hawkes processes
viscosity solution	Optimal Control of Infinite-Dimensional Differential Systems with Randomness and Path-Dependence and Stochastic Path-Dependent Hamilton–Jacobi Equations
Viscosity Solutions	Mean-Field Games in Hilbert Spaces: A Viscosity Approach
Visual sensors	Optimizing Fuzzy Partitions for Visual Sensors
Vlasov-Navier-Stokes	Intermediate Interactions in Particle Systems: Applications to Fluid Dynamics and Biological Modeling
Volterra processes	Efficient Simulation of Affine Volterra Processes Kolmogorov equations for stochastic Volterra processes with singular kernels
Volterra square-root diffusion	Explosions of stochastic Volterra equations
Volterra stochastic differential equations \and	Efficient simulation of a new class of Volterra-type SDEs
W
Walsh spider process	The Dubins Constants for Walsh's Spider Process
Wasserstein diffusion with idiosyncratic noise	Entropic Regularization of Rearranged Stochastic Heat Equation
Wasserstein distance	Quantitative Convergence of Trained Quantum Neural Networks to a Gaussian Process Theoretical guarantees for diffusion models — beyond log-concavity Approximate Bayesian computation with kernel Wasserstein distance
Wasserstein geometry	The Wasserstein geometry of random measures
Wasserstein gradient flows	Flowing Datasets with Wasserstein over Wasserstein Gradient Flows
Wasserstein Space	Massive Particle Systems, Wasserstein Brownian Motions, and the Dean--Kawasaki SPDE Mean-Field Games in Hilbert Spaces: A Viscosity Approach Wasserstein Least Squares: statistics, geometry, and algorithms
Wasserstein Spaces	Hilbert-Based Correlation Indices for Distributional Data
Weak continuity	Some results on general $\Lambda$-quantiles
Weak dependence	Accurate Bayesian inference for tail risk extrapolation in time series
Weak log-concavity	Properties of diffusion transport maps via creation of log-semiconcavity along heat flows
Weak-to-strong generalization	Learning from Surrogate Data: Weak-to-Strong Generalization through the Lens of High-Dimensional Regression
weighted triangles	Localized geometry detection in scale-free random graphs
Well-posedness	Well-posedness results and asymptotic estimates for fractional partial differential equations
White noise space	Fractional Calculus and Gaussian Processes: extensions and alternatives to fractional Brownian motion
Wick product	Wick integrals
Wide limit	Quantitative Master Theorems for Tensor Programs via the Wasserstein distance
Wiener chaos	Limit theorems for functionals of stationary Gaussian fields
Wiener process	On some drift-based transformations of multidimensional diffusion processes and their applications
Wiener process (Brownian motion)	The Wiener Disorder Problem with Random Post-Disorder Drift
Wiener-Itô chaos decomposition	New Chaos Decomposition of Gaussian Nodal Volumes
Wilson's Algorithm	Node immunization via random forests
wireless queueing analysis	Poisson Hail on a Wireless Ground
Wong-Zakai approximations	Rough differential equations for volatility
Wright--Fisher diffusion	Gamma duality and a tractable transition density for the Wright-Fisher diffusion with selection
Wright–Fisher diffusion	Multi-type logistic branching processes with selection: frequency process and genealogy for large carrying capacities
Y
Young diagram	Can one hear the shape of a random matrix?
Young Measures	Background {Vlasov} equations and {Young} measures for passive scalar and vector advection equations under special stochastic scaling limits
Z
zero-noise limit	Non-selection of Lagrangian trajectories in the zero-noise limit
Zero-noise selection	Zero-noise selection and Large Deviations in $L^\infty_t L^p_x$ for the stochastic transport equation beyond DiPerna-Lions
Zeroth-order Optimization	ZOBA: An Efficient Single-loop Zeroth-order Bilevel Optimization Algorithm
Zolotarev duality	Generalized Fractional Derivative Operators and Fractional Diffusion Equations Connected to Semistable Lévy Processes