Some Studies On A Class Of Nonlinear Delay Equations Driven By Pure Jump Processes

In this paper,we mainly focus on some properties of nonlinear delay equations driven by pure jump processes.First of all,some explicit expression for mean exit time of an simple pure jump processes are given.Second,we estimate the th moment for the solutions of stochastic nonlinear differential delay equations driven by-stable processes under the local Lipschitz condition and a kind of growth condition.In addition,we discuss the almost surely asymptotic stability of the solutions.Then,the sufficient conditions for the almost surely exponential stability of the solutions are given.Finally,we analyze the stability for the solutions of the Lotka-Volterra delay equation and Ginzburg-Landau delay equation driven by pure jump processes.