Stability Of A Class Of Delay Differential Equations Driven By Stable Processes

This paper is devoted to studying the stability for a class of stochastic delay differential equations driven by -stable processes.Firstly,we prove the existence and uniqueness of stochastic delay differential equations when the coefficients satisfy the global Lipschitz condition.Secondly,we establish the La Salle's invariance principle of the above equations.The sufficient conditions for asymptotic stability of a class of delay equations at equilibrium point are given by using the La Salle's invariance principle.In addition,we study the almost surely exponential stability of solutions for a class of stochastic delay differential equations and discuss the influence of time delay on the stability.Finally,we cite examples for geometric stable processes with a time delay to illustrate our theory.