Backward doubly SDEs and semilinear stochastic PDEs in a convex domain

Anis Matoussi, Wissal Sabbagh and Tusheng Zhang

Stochastic Processes and their Applications, 2017, vol. 127, issue 9, 2781-2815

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.

Keywords: Stochastic partial differential equation; Reflected backward doubly stochastic differential equation; Skorohod problem; Convex domains; Stochastic flow; Flow of diffeomorphisms; Regular measure (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (3)

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DOI: 10.1016/j.spa.2016.12.010

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