Moment-bounded-ness For The Solutions Of Neutral Stochastic Differential Delay Equations

This paper analyzes the connections of methods(so called Razumikhin theorem) to judge stabilities of trivial solution and bounded-ness of solutions ,which belong to Neutral Stochastic Functional Differential Equations, getting the results of similarities and differences. With the fruits, I deduce a judgment of theψr? bounded-ness of p th moment for the solutions which belong to Neutral Stochastic Functional Differential Equations. To compare with the solutions that have existed, this method is easier to use and has more practicality. As Neutral Stochastic Differential Delay Equations is the special case of Neutral Stochastic Functional Differential Equations, for that we can make full use of the judgments of the moment of trivial solution for Neutral Stochastic Functional Differential Equations that have existed ,to deduce the judgments of the bounded-ness of moment for the solutions which belong to Neutral Stochastic Functional Differential Equations, and then deduce the judgments of the bounded-ness of p th moment for the solutions belonging to Neutral Stochastic Differential Delay Equations. To compare with the solutions that have existed, this method extends the theorems, from one delay to several delays. To refine it, I divide the left of a key equation into three parts to estimate respectively. Firstly, I consider the case of second moment, and get a sufficient judgment .And then I separate the question into two situations by the value of p .At last, the paper provides two examples to demonstrate the expansibility and affectivity. .