Almost Sure Exponential Stability of Neutral Differential Difference Equations with Damped Stochastic Perturbations

摘要

In this paper we shall discuss the almost sure exponential stability for a neutral differential difference equation with damped stochastic perturbations of the form $d[x(t)-G(x(t-au))] = f(t,x(t),x(t-au))dt + sigma(t) dw(t)$. 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.