White Noise-Driven Stochastic Partial Differential Equations with Mean Reflection

Junxia Duan (), Ying Hu () and Jun Peng ()
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Junxia Duan: Henan Normal University
Ying Hu: Univ. Rennes, CNRS, IRMAR-UMR6625
Jun Peng: Central South University

Journal of Theoretical Probability, 2025, vol. 38, issue 3, 1-40

Abstract: 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.

Keywords: Stochastic partial differential equations; Mean reflection; Large deviation principle; Weak convergence method; 60H15; 60F10 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10959-025-01436-7

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