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

Xiao Xin Liao (University of Strathclyde)
Xuerong Mao (University of Strathclyde)

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.

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Pages: 1-16

Publication Date: April 15, 1996

DOI: 10.1214/EJP.v1-8

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