Electronic Journal of Probability

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

Xiao Liao and Xuerong Mao

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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.

Article information

Source
Electron. J. Probab., Volume 1 (1996), paper no. 8, 16 pp.

Dates
Accepted: 15 April 1996
First available in Project Euclid: 25 January 2016

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1453756471

Digital Object Identifier
doi:10.1214/EJP.v1-8

Mathematical Reviews number (MathSciNet)
MR1386300

Zentralblatt MATH identifier
0891.60051

Subjects
Primary: 60H10: Stochastic ordinary differential equations [See also 34F05]
Secondary: 34K20: Stability theory

Keywords
neutral equations stochastic perturbation exponential martingale inequality Borel-Cantelli's lemma Lyapunov exponent

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

Liao, Xiao; Mao, Xuerong. Almost Sure Exponential Stability of Neutral Differential Difference Equations with Damped Stochastic Perturbations. Electron. J. Probab. 1 (1996), paper no. 8, 16 pp. doi:10.1214/EJP.v1-8. https://projecteuclid.org/euclid.ejp/1453756471


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