Numerical scheme for backward doubly stochastic differential equations

Abstract

We study a discrete-time approximation for solutions of systems of decoupled forward-backward doubly stochastic differential equations (FBDSDEs). Assuming that the coefficients are Lipschitz-continuous, we prove the convergence of the scheme when the step of time discretization, $|\pi |$ goes to zero. The rate of convergence is exactly equal to $|\pi {|}^{1/2}$. The proof is based on a generalization of a remarkable result on the ${}^2$-regularity of the solution of the backward equation derived by J. Zhang

17 page; submitted to Electronic journal of Probability