Numerical Computation for Backward Doubly SDEs with random terminal time

Anis Matoussi, Wissal Sabbagh

Published 2014-09-07Version 1

In this article, we are interested in solving numerically backward doubly stochastic differential equations (BDSDEs) with random terminal time tau. The main motivations are giving a probabilistic representation of the Sobolev's solution of Dirichlet problem for semi-linear SPDEs and providing the numerical scheme for such SPDEs. Thus, we study the strong approximation of this class of BDSDEs when tau is the first exit time of a forward SDE from a cylindrical domain. We use the Euler scheme and we provide bounds for the discrete-time approximation error.