Moment Stability Of Neutral Stochastic Delay Differential Equations

Dynamical systems depend on their present and past states on common, so Neutral differential delay equations(NSDDEs)are often used to describe such systems naturely. Analyzing the stability problems of this kind of equation has important sences. This paper disscusses the pth momentψ~γstability of this kind of neutral differential delay equations.The study of NSDDEs which containing only one or two delay is common. The main aim of this paper duel with equations which contain several funtional delay. This can be used more extensive problems of SDEs. At the first, this paper mainly introduces the theory of stability, the research ground and current situation of NSDDEs and the content, the train of thought and the method of this paper. Then, the Razumikhin-Mao theorem of NSFDEs is given under a very common situation. It is more usual than the Razumikhin theorem of other documents. Then we obtain two stability results of NSDDEs. Two new theorems' conditions are more specific and practical. Following that we give an equation as an example. Based on this two theorems we obtain the stability of the zero solution of this equation. Then we compare this two methods and give some analysis. Except these, a new stability result is given. We improve the usual Lyapunov function, the solution of the equation x(t) is added. Using this new Lyapunov function, we obtain a pairing conditions about stability. This method is infrequence in other documents. Then an example is given. By this pairing conditions we give the criterion of the stability of that equation. At the same time, we also use another method which is similar to the method of the theorem 2 and made a comparion. Two corollaries are obtained. The examples make a sense that our results are practical.