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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2605.07832 |
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| _version_ | 1866917473134051328 |
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| author | Addona, Davide Masiero, Federica |
| author_facet | Addona, Davide Masiero, Federica |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_07832 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Bismut-Elworthy formula for BSDEs with degenerate noise Addona, Davide Masiero, Federica Probability 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. |
| title | A Bismut-Elworthy formula for BSDEs with degenerate noise |
| topic | Probability |
| url | https://arxiv.org/abs/2605.07832 |