A Bismut-Elworthy formula for BSDEs with degenerate noise
Probability
2026-05-11 v1
Abstract
In this paper we derive a Bismut-Elworthy formula under assumptions weaker than the 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. We also consider a nonlinear version of the Bismut formula for a backward stochastic differential equation, in analogy to what is done in \cite{futeBismut}, where a non-degenerate noise is considered. Our study is motivated by applications to stochastic wave equations and to stochastic damped wave equation.
Keywords
Cite
@article{arxiv.2605.07832,
title = {A Bismut-Elworthy formula for BSDEs with degenerate noise},
author = {Davide Addona and Federica Masiero},
journal= {arXiv preprint arXiv:2605.07832},
year = {2026}
}