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Existence and pathwise uniqueness to an SPDE driven by α-stable colored noise

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  • Xiong, Jie
  • Yang, Xu

Abstract

In this paper we study a stochastic partial differential equation (SPDE) with Hölder continuous coefficient driven by an α-stable colored noise. The pathwise uniqueness is proved by using a backward doubly stochastic differential equation backward (SDE) to take care of the Laplacian. The existence of solution is shown by considering the weak limit of a sequence of SDE system which is obtained by replacing the Laplacian operator in the SPDE by its discrete version. We also study an SDE system driven by Poisson random measures.

Suggested Citation

  • Xiong, Jie & Yang, Xu, 2019. "Existence and pathwise uniqueness to an SPDE driven by α-stable colored noise," Stochastic Processes and their Applications, Elsevier, vol. 129(8), pages 2681-2722.
    • Handle: RePEc:eee:spapps:v:129:y:2019:i:8:p:2681-2722
    DOI: 10.1016/j.spa.2018.08.003
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    References listed on IDEAS

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    1. Mytnik, Leonid & Neuman, Eyal, 2015. "Pathwise uniqueness for the stochastic heat equation with Hölder continuous drift and noise coefficients," Stochastic Processes and their Applications, Elsevier, vol. 125(9), pages 3355-3372.
    2. Fu, Zongfei & Li, Zenghu, 2010. "Stochastic equations of non-negative processes with jumps," Stochastic Processes and their Applications, Elsevier, vol. 120(3), pages 306-330, March.
    3. He, Hui & Li, Zenghu & Yang, Xu, 2014. "Stochastic equations of super-Lévy processes with general branching mechanism," Stochastic Processes and their Applications, Elsevier, vol. 124(4), pages 1519-1565.
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    Cited by:

    1. Muhammad Shoaib Arif & Kamaleldin Abodayeh & Yasir Nawaz, 2023. "A Computational Scheme for Stochastic Non-Newtonian Mixed Convection Nanofluid Flow over Oscillatory Sheet," Energies, MDPI, vol. 16(5), pages 1-17, February.
    2. Ren, Yan-Xia & Xiong, Jie & Yang, Xu & Zhou, Xiaowen, 2022. "On the extinction-extinguishing dichotomy for a stochastic Lotka–Volterra type population dynamical system," Stochastic Processes and their Applications, Elsevier, vol. 150(C), pages 50-90.
    3. Kosmala, Tomasz & Riedle, Markus, 2022. "Stochastic evolution equations driven by cylindrical stable noise," Stochastic Processes and their Applications, Elsevier, vol. 149(C), pages 278-307.

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