Malliavin differentiability of solutions of hyperbolic stochastic partial differential equations with irregular drifts
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arXiv
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| Format: | Preprint |
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2022
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| _version_ | 1866910298898694144 |
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| author | Bogso, Antoine-Marie Pamen, Olivier Menoukeu |
| author_facet | Bogso, Antoine-Marie Pamen, Olivier Menoukeu |
| contents | We prove path-by-path uniqueness of solution to hyperbolic stochastic partial differential equations when the drift coefficient is the difference of two componentwise monotone Borel measurable functions of spatial linear growth. The Yamada-Watanabe principle for SDE driven by Brownian sheet then allows to derive strong uniqueness for such equation and thus extending the results in [Bogso, Dieye and Menoukeu Pamen, Elect. J. Probab., 27:1-26, 2022] and [Nualart and Tindel, Potential Anal., 7(3):661--680, 1997]. Assuming that the drift is globally bounded, we show that the unique strong solution is Malliavin differentiable. The case of spatial linear growth drift coefficient is also studied. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_04694 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Malliavin differentiability of solutions of hyperbolic stochastic partial differential equations with irregular drifts Bogso, Antoine-Marie Pamen, Olivier Menoukeu Probability 60H07, 60H50, 60H17 We prove path-by-path uniqueness of solution to hyperbolic stochastic partial differential equations when the drift coefficient is the difference of two componentwise monotone Borel measurable functions of spatial linear growth. The Yamada-Watanabe principle for SDE driven by Brownian sheet then allows to derive strong uniqueness for such equation and thus extending the results in [Bogso, Dieye and Menoukeu Pamen, Elect. J. Probab., 27:1-26, 2022] and [Nualart and Tindel, Potential Anal., 7(3):661--680, 1997]. Assuming that the drift is globally bounded, we show that the unique strong solution is Malliavin differentiable. The case of spatial linear growth drift coefficient is also studied. |
| title | Malliavin differentiability of solutions of hyperbolic stochastic partial differential equations with irregular drifts |
| topic | Probability 60H07, 60H50, 60H17 |
| url | https://arxiv.org/abs/2210.04694 |