Almost sure exponential stability of neutral differential difference equations with damped stochastic perturbations

Abstract

In this paper we shall discuss the almost sure exponential stability for a neutral differential difference equation with damped stochastic perturbations of the form d[x(t)-G(x(t-τ))]=f(t,x(t),x(t-τ))dt+σ(t)dw(t). Several interesting examples are also given for illustration. It should be pointed out that our results are even new in the case when σ(t)≡0, i.e. for deterministic neutral differential difference equations. © 1996 Applied Probability Trust.