Successive approximation of neutral functional stochastic differential equations with variable delays

摘要

By using successive approximation, we prove the existence and uniqueness of initial value problem for stochastic differential equations driven by both the cylindrical Brownian motion and by the variable delays in a Hilbert space with non-Lipschitzian coefficients. Moreover, the numerical solutions are shown to converge uniformly to the analytical solutions of the stochastic differential equation.