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


 
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1. Title Title of document Almost Sure Exponential Stability of Neutral Differential Difference Equations with Damped Stochastic Perturbations
 
2. Creator Author's name, affiliation, country Xiao Xin Liao; University of Strathclyde
 
2. Creator Author's name, affiliation, country Xuerong Mao; University of Strathclyde
 
3. Subject Discipline(s) Mathematics
 
3. Subject Keyword(s) neutral equations, stochastic perturbation, exponential martingale inequality, Borel-Cantelli's lemma, Lyapunov exponent
 
3. Subject Subject classification 60H10, 34K2
 
4. Description 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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7. Date (YYYY-MM-DD) 1996-04-15
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/8
 
10. Identifier Digital Object Identifier 10.1214/EJP.v1-8
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 1
 
12. Language English=en en
 
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