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
Categories: math.PR