  This paper investigates a numerical probabilistic method for the solution of
some semilinear stochastic partial differential equations (SPDEs in short). The
numerical scheme is based on discrete time approximation for solutions of
systems of decoupled forward-backward doubly stochastic differential equations.
Under standard assumptions on the parameters, the convergence and the rate of
convergence of the numerical scheme is proven. The proof is based on a
generalization of the result on the path regularity of the backward equation.
