A singularly perturbed stochastic delay system with a small parameter

Abstract

A singularly perturbed stochastic delay system with wideband noise perturbations is considered in this paper. Asymptotic properties are developed. The basic mathernatical methods which are used are the martingale averaging and the techniques of the theory of weak convergence. It is shown that the limit averaged system is a diffusion process which satisfies a stochastic differential delay equation and that the correct limits hold independent of the way in which these parameters go to their limits.