Existence of strong solutions of fractional Brownian sheet driven SDEs with integrable drift
| Autor: | Bogso, Antoine-Marie, Pamen, Olivier Menoukeu, Proske, Frank |
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| Rok vydání: | 2023 |
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| Druh dokumentu: | Working Paper |
| Popis: | 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 parameter $H=(H_1,H_2)\in(0,\frac{1}{2})^2$. 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 ([Ba\~nos, 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 [Ba\~nos, Nielssen, and Proske, 2020]). Comment: 61 pages |
| Databáze: | arXiv |
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