Stability Analysis Of Neutral Stochastic Differential Delay Equations With Jumps

This dissertation mainly discusses the existence and uniqueness,the stability of global solutions of neutral stochastic delay differential equation driven by the Lévy process and neutral stochastic markov delay differential equation driven by the Lévy process.For the first system,in order to overcome the difficulty from the existence of the fast time-varying delay(time varying delay is bounded),one integral lemma is established,and the existence and uniqueness,the pth(p?2)-moment exponential stability and almost surely asymptotic stability of the first equation are discussed.For the second equation,an auxiliary equation is introduced in this paper,and Lyapunov function method and comparison principle are used.A upper bound of maximum admissible delay ?*and the corresponding upper bound of maximum admissible contractive coefficient ?*of the second equation are obtained.The specific chapters of this paper are as follows:In the first chapter,this paper mainly discusses the background of this study,basic definition,main innovation points and some necessary knowledge.In chapter 2,this paper mainly discusses the existence and uniqueness of global solution,the pth(p? 2)-moment exponential stability and the almost surely exponential stability of neutral stochastic delay differential equation driven by Lévy processes.In the third chapter,by using comparison principle and Lyapunov function method,by introducing an auxiliary equation(a stochastic Markovian delay system driven by Lévy process),this paper studies almost surely exponential stability of neutral stochastic Markovian delay differential equation driven by Lévy process.In the fourth chapter,the conclusion of the stability analysis of two equation and the prospect of the future research are summarized.