Some Results Of Nonlinear Volterra Stochastic Functional Differential Equations

This paper is divided into 3 chapters. In chapter 1 , we introduce to some background of stochastic differential equations and the preliminary which include some notations and basic theory that we want to use, also, we introduce to some related results in the past and the definitions and lemma that we apply to proof the theorem in this paper. the chapter 2 is the main body of the paper. Firstly, we show the existence-and-uniqueness condition of the equations that we want to discuss. Secondly, we obtain some results of stability and boundedness,which include sufficient conditions for mean square asymptotical stability and almost sure expontential stability of zero solution. In chapter 3, some examples and graphs will be given to validate the theorem we have.At the end of this paper, the author summarizes the innovations and proposes the direction of future work. Finally, related literatures are listed.