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<p>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).</p>

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

  • 期刊论文

  • 发表日期：

    2025年12月12日

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  • Antoine-Marie Bogso,
  • Olivier Menoukeu Pamen,
  • Frank Norbert Proske

摘要

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).