Coupling of forward-backward stochastic differential equations on the Wiener space, and application on regularity
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866908405055094784 |
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| author | Zhou, Xilin |
| author_facet | Zhou, Xilin |
| contents | S. Geiss and J. Ylinen proposed the coupling method \cite{Geiss:Ylinen:21} to investigate the regularity for the solution to the backward stochastic differential equations with random coefficients. In this paper, we explore this method in setting for the forward-backward stochastic differential equation with random and Lipschitz coefficients, We obtain the regularity in time, and the Malliavin Sobolev ${\mathbb D}_{1,2}$ differentiability for the solution. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_10213 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Coupling of forward-backward stochastic differential equations on the Wiener space, and application on regularity Zhou, Xilin Probability 60H07, 60H10, 46E35 S. Geiss and J. Ylinen proposed the coupling method \cite{Geiss:Ylinen:21} to investigate the regularity for the solution to the backward stochastic differential equations with random coefficients. In this paper, we explore this method in setting for the forward-backward stochastic differential equation with random and Lipschitz coefficients, We obtain the regularity in time, and the Malliavin Sobolev ${\mathbb D}_{1,2}$ differentiability for the solution. |
| title | Coupling of forward-backward stochastic differential equations on the Wiener space, and application on regularity |
| topic | Probability 60H07, 60H10, 46E35 |
| url | https://arxiv.org/abs/2506.10213 |