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Stability of a Neutral Stochastic Functional Differential Equations
Authors:Li Bi-wen
Affiliation:(1) Department of Mathematics, Hubei Normal University, 135002 Huangshi, Hubei, China;(2) Department of Mathematics, Huazhong University of Science and Technology, 430074 Wuhan, Hubei, China
Abstract:Sufficient condition for stochastic unifrom stability of a neutral stochastic functional differential equation is given, especially, new techniques are developed to cope with the neutral delay case, we obtained the sufficient condition for asymptotic stability of neutral stochastic differential delay equations. Due to the new techniques developed in this paper, the results obtained arc very general and useful. The theory developed here gives a unified treatment for various asymptotic estimates e.g. exponential and polynomial bounds.
Keywords:Lyapunov function   D operator  It?’  s formula  stochastic unifrom stabillty  asymptotic stability
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