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System of Reflected Stochastic PDEs in a domain

We are interested in solving a system of reflected stochastic PDEs in a domain (known as Skorohod problem). The solution is expressed as a pair (u,\mu), where u is a predictable continuous process which takes values in a Sobolev space and \mu is a random regular measure. The main purpose is giving the probabilistic representation of this pair (u,\mu) via the associated solution of reflected BSDEs. In a second part, numerical scheme for backward doubly stochastic differential equations with random terminal time is developed in order to provide a Monte Carlo scheme for a class of semilinear SPDEs with Cauchy-Dirichlet condition in some domain.

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