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Existence and uniqueness of SPDEs driven by nonlinear multiplicative mixed noise

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  • Qu, Shiduo
  • Gao, Hongjun

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.

Suggested Citation

  • Qu, Shiduo & Gao, Hongjun, 2025. "Existence and uniqueness of SPDEs driven by nonlinear multiplicative mixed noise," Stochastic Processes and their Applications, Elsevier, vol. 184(C).
    • Handle: RePEc:eee:spapps:v:184:y:2025:i:c:s0304414925000535
    DOI: 10.1016/j.spa.2025.104612
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