Bismut Formula and Gradient Estimates for Dirichlet Semigroups with Application to Singular Killed DDSDEs
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866914426170376192 |
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| author | Wang, Feng-Yu Zhao, Xiao-Yu |
| author_facet | Wang, Feng-Yu Zhao, Xiao-Yu |
| contents | By establishing a local version of Bismut formula for Dirichlet semigroups on a regular domain, gradient estimates are derived for killed SDEs with singular drifts. As an application, the total variation distance between two solutions of killed DDSDEs is bounded above by the truncated $1$-Wasserstein distance of initial distributions, in the regular and singular cases respectively. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_19429 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Bismut Formula and Gradient Estimates for Dirichlet Semigroups with Application to Singular Killed DDSDEs Wang, Feng-Yu Zhao, Xiao-Yu Probability 60B05, 60B10 By establishing a local version of Bismut formula for Dirichlet semigroups on a regular domain, gradient estimates are derived for killed SDEs with singular drifts. As an application, the total variation distance between two solutions of killed DDSDEs is bounded above by the truncated $1$-Wasserstein distance of initial distributions, in the regular and singular cases respectively. |
| title | Bismut Formula and Gradient Estimates for Dirichlet Semigroups with Application to Singular Killed DDSDEs |
| topic | Probability 60B05, 60B10 |
| url | https://arxiv.org/abs/2506.19429 |