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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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    References listed on IDEAS

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    1. José Luís Silva & Mohamed Erraoui & El Hassan Essaky, 2018. "Mixed Stochastic Differential Equations: Existence and Uniqueness Result," Journal of Theoretical Probability, Springer, vol. 31(2), pages 1119-1141, June.
    2. Kubilius, K., 2002. "The existence and uniqueness of the solution of an integral equation driven by a p-semimartingale of special type," Stochastic Processes and their Applications, Elsevier, vol. 98(2), pages 289-315, April.
    3. Shevchenko, Georgiy & Shalaiko, Taras, 2013. "Malliavin regularity of solutions to mixed stochastic differential equations," Statistics & Probability Letters, Elsevier, vol. 83(12), pages 2638-2646.
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