Exponential Stability And Approximate Controllability Of Impulsive Stochastic Functional Differential Equations

In this paper, we investigate the impulsive stochastic systems mainly by the theory of semigroups. First of all, we prove the existence and uniqueness of the mild solutions for the systems in Hilbert spaces by Banach Fixed Point Theorem. Then we discuss the exponential stability of the first system and the approximate controllability of the second system, respectively.The whole paper is divided into four parts. In Chapter 1, we simply introduce the background and the significance of our research; Chapter 2 provides some fundamental definitions, signals and basic theories about stochastic processes and analytic semigroups, which will be used in this paper; Chapter 3 is devoted to the existence, uniqueness and exponential stability of the solutions, and Chapter 4 of this paper is devoted to the approximate controllability of the second system, an example is provided at last in each chapter.