Backward doubly SDEs and semilinear stochastic PDEs in a convex domain

Research output: Contribution to journalArticle

  • Authors:
  • Anis Matoussi
  • Wissal Sabbagh
  • Tusheng Zhang

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.

Bibliographical metadata

Original languageEnglish
JournalStochastic Processes and their Applications
Early online date17 Jan 2017
DOIs
StatePublished - 2017