What does this research mean for the field?

A regularization-based framework for stochastic integration with respect to multidimensional fractional Brownian sheets is equivalent to the Malliavin calculus construction and establishes well-posedness and regularity for anisotropic stochastic partial differential equations. Novelty: ClaimNovelty.METHODOLOGICAL. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

To establish a rigorous stochastic integration framework for multidimensional, anisotropic fractional Brownian sheets with Hurst parameters exceeding one-half and analyze associated stochastic partial differential equations.

August 22, 2026Science Journal of Applied Mathematics and StatisticsOpen Access

Stochastic Integration with Respect to Fractional Brownian Sheets and Applications to Anisotropic SPDEs

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To establish a rigorous stochastic integration framework for multidimensional, anisotropic fractional Brownian sheets with Hurst parameters exceeding one-half and analyze associated stochastic partial differential equations.
Developed a regularization-based integration approach reflecting directional heterogeneity and proved its mean-square convergence to the Skorokhod integral via Malliavin calculus.
Established well-posedness of anisotropic SPDEs using a fixed-point argument in tailored solution spaces.
Derived solution regularity using an anisotropic formulation of the Kolmogorov continuity criterion.
Demonstrated mathematical equivalence and duality relations between the regularized stochastic integral and Malliavin-Skorokhod analytical frameworks.
Obtained well-posedness and Hölder continuity exponents that directly reflect the directional smoothness and Hurst indices of the driving noise sheet.

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Implication

Theoretical analysis establishes integration frameworks for anisotropic fractional Brownian sheets, indicating robust modeling tools for systems with directional memory.

Cite This Study

Bou Diop (2026) studied this question.

synapsesocial.com/papers/6a895fe4ca7ade938187ed64 https://doi.org/10.11648/j.sjams.20261404.12

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Implication

Theoretical analysis establishes integration frameworks for anisotropic fractional Brownian sheets, indicating robust modeling tools for systems with directional memory.

Stochastic Integration with Respect to Fractional Brownian Sheets and Applications to Anisotropic SPDEs

Key Points

Discussion

Implication

Cite This Study

Stochastic Integration with Respect to Fractional Brownian Sheets and Applications to Anisotropic SPDEs

Key Points

Discussion

Implication

Cite This Study

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