Strong solutions of fractional Brownian sheet driven SDEs with integrable drift

Antoine-Marie Bogso; Olivier Menoukeu Pamen; Frank Proske

doi:10.1007/s10959-025-01470-5

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arXiv · 2307.09086

Strong solutions of fractional Brownian sheet driven SDEs with integrable drift

Antoine-Marie Bogso·Olivier Menoukeu Pamen·Frank Proske

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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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Antoine-Marie Bogso, Olivier Menoukeu Pamen, Frank Proske. 2023-07-18. Strong solutions of fractional Brownian sheet driven SDEs with integrable drift. https://doi.org/10.1007/s10959-025-01470-5

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