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 ([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]).

60 pages

References in corpus (2)

• Malliavin differentiability of solutions of hyperbolic stochastic partial differential equations with irregular drifts
• Smoothness of solutions of hyperbolic stochastic partial differential equations with $L^{\infty }$-vector fields