Strong solutions of fractional Brownian sheet driven SDEs with integrable drift
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866914200771624960 |
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| author | Bogso, Antoine-Marie Pamen, Olivier Menoukeu Proske, Frank |
| author_facet | Bogso, Antoine-Marie Pamen, Olivier Menoukeu Proske, Frank |
| contents | We prove the existence of a unique Malliavin differentiable strong solution to a stochastic differential equation on the plane with merely integrable coefficients driven by the fractional Brownian sheet with Hurst parameters less than 1/2. The proof of this result relies on a compactness criterion for square integrable Wiener functionals from Malliavin calculus ([Da Prato, Malliavin and Nualart, 1992]), variational techniques developed in the case of fractional Brownian motion ([Baños, Nielssen, and Proske, 2020]) and the concept of sectorial local nondeterminism (introduced in [Khoshnevisan and Xiao, 2007]). The latter concept enable us to improve the bound of the Hurst parameter (compare with [Baños, Nielssen, and Proske, 2020]). |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2307_09086 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Strong solutions of fractional Brownian sheet driven SDEs with integrable drift Bogso, Antoine-Marie Pamen, Olivier Menoukeu Proske, Frank Probability 60H07, 60H50, 60H17 We prove the existence of a unique Malliavin differentiable strong solution to a stochastic differential equation on the plane with merely integrable coefficients driven by the fractional Brownian sheet with Hurst parameters less than 1/2. The proof of this result relies on a compactness criterion for square integrable Wiener functionals from Malliavin calculus ([Da Prato, Malliavin and Nualart, 1992]), variational techniques developed in the case of fractional Brownian motion ([Baños, Nielssen, and Proske, 2020]) and the concept of sectorial local nondeterminism (introduced in [Khoshnevisan and Xiao, 2007]). The latter concept enable us to improve the bound of the Hurst parameter (compare with [Baños, Nielssen, and Proske, 2020]). |
| title | Strong solutions of fractional Brownian sheet driven SDEs with integrable drift |
| topic | Probability 60H07, 60H50, 60H17 |
| url | https://arxiv.org/abs/2307.09086 |