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White Noise-Driven Stochastic Partial Differential Equations with Mean Reflection

Author

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  • Junxia Duan

    (Henan Normal University)

  • Ying Hu

    (Univ. Rennes, CNRS, IRMAR-UMR6625)

  • Jun Peng

    (Central South University)

Abstract

In this paper, we study a new type of SPDEs with reflection (called mean reflected stochastic partial differential equations (SPDEs)), where the compensating reflection part depends not on the paths but on the law of the solution. Focusing on solutions (u, K) with deterministic K, we obtain the well-posedness of such SPDEs. Utilizing the weak convergence approach, we then establish large deviation principles for this type of SPDEs.

Suggested Citation

  • Junxia Duan & Ying Hu & Jun Peng, 2025. "White Noise-Driven Stochastic Partial Differential Equations with Mean Reflection," Journal of Theoretical Probability, Springer, vol. 38(3), pages 1-40, September.
    • Handle: RePEc:spr:jotpro:v:38:y:2025:i:3:d:10.1007_s10959-025-01436-7
    DOI: 10.1007/s10959-025-01436-7
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    References listed on IDEAS

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    1. Briand, Philippe & Cardaliaguet, Pierre & Chaudru de Raynal, Paul-Éric & Hu, Ying, 2020. "Forward and backward stochastic differential equations with normal constraints in law," Stochastic Processes and their Applications, Elsevier, vol. 130(12), pages 7021-7097.
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    5. Cardon-Weber, Caroline, 1999. "Large deviations for a Burgers'-type SPDE," Stochastic Processes and their Applications, Elsevier, vol. 84(1), pages 53-70, November.
    6. 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.
    7. 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.
    8. Philippe Briand & Romuald Elie & Ying Hu, 2018. "BSDEs with mean reflection," Post-Print hal-01318649, HAL.
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    Full references (including those not matched with items on IDEAS)

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