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Reflected backward stochastic partial differential equations with jumps in a convex domain

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  • Yang, Xue

Abstract

This paper is concerned with a class of multi-dimensional reflected backward stochastic partial differential equations (BSPDE for short), taking values in a convex domain in Rk, which are driven by an infinite dimensional Brownian motion and an independent compensated Poisson random measure. Existence and uniqueness of the solution to this class of reflected BSPDEs are proved. Penalization method plays an important role.

Suggested Citation

  • Yang, Xue, 2019. "Reflected backward stochastic partial differential equations with jumps in a convex domain," Statistics & Probability Letters, Elsevier, vol. 152(C), pages 126-136.
    • Handle: RePEc:eee:stapro:v:152:y:2019:i:c:p:126-136
    DOI: 10.1016/j.spl.2019.04.019
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    References listed on IDEAS

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    1. Bernt Øksendal & Agnès Sulem & Tusheng Zhang, 2014. "Singular Control and Optimal Stopping of SPDEs, and Backward SPDEs with Reflection," Mathematics of Operations Research, INFORMS, vol. 39(2), pages 464-486, May.
    2. Matoussi, Anis & Sabbagh, Wissal & Zhang, Tusheng, 2017. "Backward doubly SDEs and semilinear stochastic PDEs in a convex domain," Stochastic Processes and their Applications, Elsevier, vol. 127(9), pages 2781-2815.
    3. Xu, Tiange & Zhang, Tusheng, 2009. "White noise driven SPDEs with reflection: Existence, uniqueness and large deviation principles," Stochastic Processes and their Applications, Elsevier, vol. 119(10), pages 3453-3470, October.
    4. Zhang, Tusheng, 2011. "Systems of stochastic partial differential equations with reflection: Existence and uniqueness," Stochastic Processes and their Applications, Elsevier, vol. 121(6), pages 1356-1372, June.
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    Cited by:

    1. Yang, Xue & Zhang, Qi & Zhang, Tusheng, 2020. "Reflected backward stochastic partial differential equations in a convex domain," Stochastic Processes and their Applications, Elsevier, vol. 130(10), pages 6038-6063.

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