Stability of a Neutral Stochastic Functional Differential Equations

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 stabillty of neutral stochastic differential delay equations. Due to the new techniques developed in this paper, the results obtained are very general and useful. The theory developed here gives a unified treatment for various asymptotic estimates e.g. exponential and polynomial bounds.