Some analytic approximations for neutral stochastic functional differential equations
Abstract We consider an analytic iterative method to approximate the solution of a neutral stochastic functional differential equation. More precisely, we define a sequence of approximate equations and we give sufficient conditions under which the approximate solutions converge with probability one and in p th moment sense, p  ⩾ 2, to the solution of the initial equation. We introduce the notion of the Z -algorithm for this iterative method and present some examples to illustrate the theory. Especially, we point out that the well-known Picard method of iterations is a special Z -algorithm.