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Backward doubly SDEs and semilinear stochastic PDEs in a convex domain

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  • Matoussi, Anis
  • Sabbagh, Wissal
  • Zhang, Tusheng

Abstract

This paper presents existence and uniqueness results for reflected backward doubly stochastic differential equations (in short RBDSDEs) in a convex domain D without any regularity conditions on the boundary. Moreover, using a stochastic flow approach a probabilistic interpretation for a system of reflected SPDEs in a domain is given via such RBDSDEs. The solution is expressed as a pair (u,ν) where u is a predictable continuous process which takes values in a Sobolev space and ν is a random regular measure. The bounded variation process K, the component of the solution of the reflected BDSDE, controls the set when u reaches the boundary of D. This bounded variation process determines the measure ν from a particular relation by using the inverse of the flow associated to the diffusion operator.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:spapps:v:127:y:2017:i:9:p:2781-2815
    DOI: 10.1016/j.spa.2016.12.010
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    References listed on IDEAS

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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.
    2. 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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