Numerical scheme for a semilinear Stochastic PDEs via Backward Doubly Stochastic Differential Equations

Achref Bachouch, Mohamed Anis Ben Lasmar, Anis Matoussi, Mohamed Mnif

Published 2013-02-03, updated 2014-09-22Version 5

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