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Almost sure exponential stability of neutral differential difference equations with damped stochastic perturbations. (English) Zbl 0891.60051

Summary: We 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.

MSC:

60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
34K20 Stability theory of functional-differential equations
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