Existence and uniqueness of SPDEs driven by nonlinear multiplicative mixed noise

Shiduo Qu and Hongjun Gao

Stochastic Processes and their Applications, 2025, vol. 184, issue C

Abstract: This paper investigates a class of stochastic partial differential equations (SPDEs) driven by standard Brownian motion and fractional Brownian motion with Hurst parameter H>1/2. We establish the existence and uniqueness of solutions for these SPDEs in sense of almost surely. We further prove that the moments of the solutions are finite. Moreover, we explore the equivalence between the integral defined by fractional derivatives and that defined by sewing lemma.

Keywords: Stochastic partial differential equations; Fractional Brownian motion; Mixed noise (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1016/j.spa.2025.104612

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