A Bismut-Elworthy formula for BSDEs with degenerate noise

Davide Addona; Federica Masiero

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arXiv · 2605.07832

A Bismut-Elworthy formula for BSDEs with degenerate noise

Davide Addona·Federica Masiero

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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.

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BibTeX RIS

Davide Addona, Federica Masiero. 2026-05-08. A Bismut-Elworthy formula for BSDEs with degenerate noise. https://arxiv.org/abs/2605.07832

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