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
$sigma(t) eq 0$, i.e. for deterministic neutral differential
difference equations.
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