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Mean reflected backward stochastic partial differential equations

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  • Qian, Hongchao

Abstract

This paper is concerned with a class of one-dimensional mean reflected backward stochastic partial differential equations (MRBSPDEs). In our framework, the constraint depends on the law of the solution rather than on its paths. Specifically, the compensating reflection part keeps the expectation of the solution above a given deterministic function. The existence and uniqueness of solution are established by a penalty method.

Suggested Citation

  • Qian, Hongchao, 2026. "Mean reflected backward stochastic partial differential equations," Statistics & Probability Letters, Elsevier, vol. 229(C).
    • Handle: RePEc:eee:stapro:v:229:y:2026:i:c:s0167715225002251
    DOI: 10.1016/j.spl.2025.110580
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    References listed on IDEAS

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    1. Falkowski, Adrian & Słomiński, Leszek, 2021. "Mean reflected stochastic differential equations with two constraints," Stochastic Processes and their Applications, Elsevier, vol. 141(C), pages 172-196.
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    4. Miryana Grigorova & Peter Imkeller & Elias Offen & Youssef Ouknine & Marie-Claire Quenez, 2015. "Reflected BSDEs when the obstacle is not right-continuous and optimal stopping," Papers 1504.06094, arXiv.org, revised May 2017.
    5. 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.
    6. 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.
    7. Ruimin Xu & Tingting Wu, 2014. "Mean-Field Backward Stochastic Evolution Equations in Hilbert Spaces and Optimal Control for BSPDEs," Mathematical Problems in Engineering, Hindawi, vol. 2014, pages 1-18, July.
    8. 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.
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