Strong solutions of fractional Brownian sheet driven SDEs with integrable drift
Abstract
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 ([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]).
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Cite
@article{arxiv.2307.09086,
title = {Strong solutions of fractional Brownian sheet driven SDEs with integrable drift},
author = {Antoine-Marie Bogso and Olivier Menoukeu Pamen and Frank Proske},
journal= {arXiv preprint arXiv:2307.09086},
year = {2025}
}
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60 pages