Strong solutions of fractional Brownian sheet driven SDEs with integrable drift

2023/07/18 by Antoine-Marie Bogso, Bogso, Antoine-Marie, Olivier Menoukeu Pamen +3
Economics, Econometrics and Finance · Engineering · Social Sciences · #60H07 #60H17 #60H50 #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Insurance, Mortality, Demography, Risk Management #Probability (math.PR) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2307.09086

openalex publication_date 2023/07/18 · openalex created_date 2023/07/20 · openalex updated_date 2026/07/30

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]).

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