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

Jie Xiong and Xu Yang

Stochastic Processes and their Applications, 2019, vol. 129, issue 8, 2681-2722

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.

Keywords: Stochastic partial differential equation; Colored noise; Stable; Existence; Pathwise uniqueness (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:129:y:2019:i:8:p:2681-2722

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DOI: 10.1016/j.spa.2018.08.003

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