Regularity of stochastic differential equations on the Wiener space by coupling
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866916745576448000 |
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| author | Geiss, Stefan Zhou, Xilin |
| author_facet | Geiss, Stefan Zhou, Xilin |
| contents | Using the coupling method introduced in \cite{Geiss:Ylinen:21}, we investigate regularity properties of stochastic differential equations, where we consider the Lipschitz case in $\R^d$ and allow for Hölder continuity of the diffusion coefficient of scalar valued stochastic differential equations. Two cases of the coupling method are of special interest: The uniform coupling to treat the Malliavin Sobolev space $\D_{1,2}$ and real interpolation spaces, and secondly a cut-off coupling to treat the $L_p$-variation of backward stochastic differential equations where the forward process is the investigated stochastic differential equation. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2412_10836 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Regularity of stochastic differential equations on the Wiener space by coupling Geiss, Stefan Zhou, Xilin Probability 60H07, 60H10, 46E35, 46B70 Using the coupling method introduced in \cite{Geiss:Ylinen:21}, we investigate regularity properties of stochastic differential equations, where we consider the Lipschitz case in $\R^d$ and allow for Hölder continuity of the diffusion coefficient of scalar valued stochastic differential equations. Two cases of the coupling method are of special interest: The uniform coupling to treat the Malliavin Sobolev space $\D_{1,2}$ and real interpolation spaces, and secondly a cut-off coupling to treat the $L_p$-variation of backward stochastic differential equations where the forward process is the investigated stochastic differential equation. |
| title | Regularity of stochastic differential equations on the Wiener space by coupling |
| topic | Probability 60H07, 60H10, 46E35, 46B70 |
| url | https://arxiv.org/abs/2412.10836 |