ON THE GENERALIZED Z-ALGORITHM FOR THE NEUTRAL STOCHASTIC FUNCTIONAL DIFFERENTIAL EQUATIONS WITH INFINITE DELAY

摘要

For any d-dimensional neutral stochastic functional differential equation with infinite delay and m-dimensional Brownian motion, we introduce a sequence of approximate equations and offer sufficient conditions such that the approximate solutions converge with probability one to the solution of the given equation. This iterative method called the generalized Z-algorithm is a generalization to many well-known analytic iterative method.