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<p>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 (<i>u</i>,&#xa0;<i>K</i>) with deterministic <i>K</i>, we obtain the well-posedness of such SPDEs. Utilizing the weak convergence approach, we then establish large deviation principles for this type of SPDEs.</p>

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White Noise-Driven Stochastic Partial Differential Equations with Mean Reflection

  • 期刊论文

  • 发表日期：

    2025年8月18日

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  • Junxia Duan,
  • Ying Hu,
  • Jun Peng

摘要

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.