On Some Problems For Stability Of Stochastic Delay Differential Equations

Many phenomenons in nature are stochastic, have been influenced by random factors. Stochastic differential equation is a research field which has the value of theory and the background of application, stability of solution is an important problem in the theory of stochastic differential equation.This Ph.D. thesis is composed of three chapters, which mainly studied the pth moment exponential stability criteria of neutral stochastic functional differential equations with im-pulsive jumps and exponential stability criteria for stochastic delay partial differential equa-tions.In the first chapter, we introduced the history background of problems which will be investigated and main results of this paper.In Chapter 2, we discussed the pth moment exponential stability criteria of neutral stochastic functional differential equations with impulsive jumps. By employing the analysis technique and Lyapunov functions, Several pth moment exponential stability criteria are established. Since the solution of the equations is discontinuous, we shall overcome the difficulty, some known results are generalized. An illustrative example is given to show the effectiveness of our results.In Chapter 3, we mainly studied exponential stability criteria for stochastic delay partial differential equations. This paper is concerned with the exponential stability of energy solutions to a nonlinear stochastic delay partial differential equations with finite delay in separable Hilbert spaces. Some exponential stability criteria are obtained by constructing the Lyapunov function. As an application, two examples are given to illustrate our results.