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 $d[x(t)-G(x(t-\tau))] = f(t,x(t),x(t-\tau))dt + \sigma(t) dw(t)$. Several interesting examples are also given for illustration. It should be pointed out that our results are even new in the case when $\sigma(t) \equiv 0$, i.e. for deterministic neutral differential difference equations.