Backward doubly SDEs and semilinear stochastic PDEs in a convex domain - Archive ouverte HAL
Article Dans Une Revue Stochastic Processes and their Applications Année : 2017

Backward doubly SDEs and semilinear stochastic PDEs in a convex domain

Anis Matoussi
Wissal Sabbagh
Tusheng Zhang
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Résumé

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 the diffusion operator.
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Dates et versions

hal-01740652 , version 1 (22-03-2018)

Identifiants

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Anis Matoussi, Wissal Sabbagh, Tusheng Zhang. Backward doubly SDEs and semilinear stochastic PDEs in a convex domain. Stochastic Processes and their Applications, 2017, 127 (9), pp.2781-2815. ⟨10.1016/j.spa.2016.12.010⟩. ⟨hal-01740652⟩
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