Strong Solutions of Fractional Brownian Sheet-Driven Stochastic Differential Equations with Integrable Drift

Antoine-Marie Bogso (), Olivier Menoukeu Pamen () and Frank Norbert Proske ()
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Antoine-Marie Bogso: University of Yaounde 1, Department of Mathematics
Olivier Menoukeu Pamen: University of Liverpool, Department of Mathematical Sciences
Frank Norbert Proske: University of Oslo, Department of Mathematical Sciences

Journal of Theoretical Probability, 2026, vol. 39, issue 1, 1-49

Abstract: Abstract We prove the existence of a unique Malliavin differentiable strong solution to a stochastic differential equation on the plane with merely integrable coefficients and 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 in CR Acad Sci Paris Série 1, Mathématique 315:1287–1291, 1992), variational techniques developed in the case of fractional Brownian motion (Baños in J Dyn Diff Equat 32:1819–1866, 2020) and the concept of sectorial local nondeterminism introduced by Khoshnevisan (Khoshnevisan in Trans Amer Math Soc 359:3125–3151, 2007). The latter concept enables us to improve the bound of the Hurst parameter; compare with (Baños in J Dyn Diff Equat 32:1819–1866, 2020).

Keywords: Plane SDEs; Fractional Brownian sheet; Sectorial local nondeterminism; Malliavin calculus; 60H07; 60H50; 60H17; 60H15 (search for similar items in EconPapers)
Date: 2026
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DOI: 10.1007/s10959-025-01470-5

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