Some analytic approximations for backward stochastic differential equations

Abstract

We consider an analytic iterative method to approximate the solution of the backward stochastic differential equation of general type. More pre- cisely, we define a sequence of approximate equations and give sufficient conditions under which the approximate solutions converge with proba- bility one and in pth moment sense, p ≥ 2, to the solution of the initial equation under Lipschitz condition. The Z-algorithm for this iterative method is introduced and some examples are presented to illustrate the theory.