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

   
@article{EJP8,
	author = {Xiao Liao and Xuerong Mao},
	title = {Almost Sure Exponential Stability of Neutral Differential Difference Equations with Damped Stochastic Perturbations},
	journal = {Electron. J. Probab.},
	fjournal = {Electronic Journal of Probability},
	volume = {1},
	year = {1996},
	keywords = {neutral equations, stochastic perturbation, exponential martingale inequality, Borel-Cantelli's lemma, Lyapunov exponent},
	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.},
	pages = {no. 8, 1-16},
	issn = {1083-6489},
	doi = {10.1214/EJP.v1-8},    
        url = {http://ejp.ejpecp.org/article/view/8}}