  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 semilinear 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. Euler schemes and bounds for the discrete-time approximation error are
provided.
