Stability Analysis Of Neutral Stochastic Differential Equations With Distributed Time-varying Delay

In this paper,we will devote on the existence and uniqueness,the stability of the solution for neutral stochastic differential equations(NSDDE)with distributed time-varying delay and Markovian switching,and for NSDDE with distributed time-varying delay,respectively.For the first system,in order to overcome the influence of distributed delay on the system,one integral inequality is firstly established.Then the pth(p>1)-moment exponential stability and the almost sure stability are discussed.For the second system,establishing an auxiliary system,using the comparison principle and the Lyapunov function approach,the upper bound ?*being determined.,and to fix the upper limit of ?*then obtain the corresponding value of the compression coefficient k*.The details are as follows:Chapter 1 Research background and significance,main innovations and preliminary knowledge of the thesis.Chapter 2 Establishing an integral lemma by utilizing a Lyapunov function.Under a locally Lipschitz condition,a monotonicity condition and a contractive condition,the existence and uniqueness theorem for the global solution of NSDDE with distributed time-varying delay is proved by using the stopping time technique.Then employing the Lyapunov function and the inequality technique,the pth(p>1)-moment exponential stability is discussed.Besides,by establishing an integral inequality and using the nonnegative semi-martingale convergence theorem,the almost sure stability is also analyzed.Chapter 3 Investigating the problem on the stability analysis of NSDDE with distributed time-varying delay by using the Lyapunov function incorporating with the comparison principle.One stochastic delay differential equation(SDDE)with distributed time-varying delay is taken as the auxiliary equation.If the stochastic differential equation(SDE)is pth(p? 2)-moment exponential stability,the pth(p? 2)-moment exponential stability for SDDE is first proved with the upper bound ?*being determined for time-varying delay.Then,fixing the upper bound ?*,the corresponding value k*of the contractive coefficient is also obtained to guarantee the pth(p? 2)-moment exponential stability of NSDDE with distributed time-varying delay.Chapter 4 Summarizes the conclusions obtained in this paper and looks forward to future research directions.