\title{Bismut-Elworthy type formulae for BSDEs with degenerate noise }

% Author name(s) \author{ Davide Addona\inst{2} \and Federica Masiero\inst{1}\thanks{Presenter} %\and %Third Author\inst{2} } % % \institute{Department of Mathematics and Applications, University of Milano Bicocca, Italy, \\ \email{federica.masiero@unimib.it}\\ \and Department of Mathematical, Physical and Computer Sciences, University of Parma, Parma, Italy\\ \email{davide.addona}@unipr.it}

% \maketitle %

\keywords{gradient estimates \and degenerate noise \and backward stochastic differential equations} \\

In this talk we present how to derive Bismut-Elworthy formula under assumptions weaker than non degeneracy of the noise. By Bismut-Elworthy formula we mean a gradient type estimate on the transition semigroup of a stochastic differential equation in a possibly infinite dimensional Hilbert space. \newline We also present a nonlinear version of the Bismut formula for BSDEs, in analogy to what is done in \cite{FT} in the case of non degenerate noise, and we discuss applications to the solution of semilinear Kolmogorov equations.

Our study is motivated by the regularizing properities of the transition semigroup of the stochastic wave equations, studied in \cite{MP}, and of the stochastic damped wave equation, first studied in \cite{AddBig24} and next also in \cite{AddMas}.

\def\sessionnumber{CS124}

\def\sessionname{Infinite Dimensional Analysis and Malliavin Calculus}

\def\firstorganizer{Davide Addona}