The Stability Of Neutral Impulsive Stochastic Differential Equation

This paper mainly discusses the stability of neutral stochastic differential equations with impulsive effect. Applying the theories of stochastic analysis and stability of stochastic differential equation, and employing some inequalities of elementary mathematics and methods of elementary mathematics, this paper proposes the conditions of mean square stability, pth moment stability and mean square exponential stability for neutral stochastic differential equations with impulsive effect, respectively. The whole thesis is divided into four chapters.The first chapter, the investigated background and significance for neutral stochastic differential equations with impulsive effect are illustrated. The research status of neutral stochastic differential equations with impulsive effect is reviewed. The mainly investigated contents and methods are introduced.The second chapter, based on Ito s’ formula, Lyapunov function and Holder inequality, this paper studies the mean square stability, p moment stability and mean square exponential stability for neutral stochastic differential equations with impulsive effect, and the stability conditions are provided.The third chapter, applying Ito s’ formula, Lyapunov function, Holder inequality and some conclusions in the second chapter, this paper discusses the mean square stability, pth moment stability and mean square exponential stability for neutral stochastic linear differential equations with impulsive effect, and the stability conditions are gave.The fourth chapter, the main research contents of this paper are summed up. An outlook for further research is put forward.