Some Analytic Approximations for Backward Stochastic Differential Equations

We consider an analytic iterative method to approximate the solution of the backward stochastic differential equation of general type. More precisely, we define a sequence of approximate equations and give sufficient conditions under which the approximate solutions converge with probability 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.