General Stability Of Neutral Stochastic Functional Differential Equations Driven By Lévy Noise

Randomness and time delay are universal phenomena in natural and social practice,they often make many dynamic systems fail to work,namely instable or even corrupted phenomenon would occur.Therefore,the stability of stochastic time-delay differential system has been a hot topic,and many important research results have been obtained.However,there are many dynamic systems which would not only be affected by randomness and time delay but also affected by sudden disturbances and impact from outside,leading to the big jumping,so,the traditional stochastic delay differential systems can not fit to describe these realistic systems,the stochastic delay differential equations driven by Lévy noises or Poisson jumping can fit these systems well,so,the study of stability about these dynamic systems has attracted many scholar's attention in recent years.Then,the most study of stability is limited to exponential stability,however,in reality,most of the stochastic differential systems are not convergent exponentially,but at the rate of lower than it,so,some scholars put forward the concept of the general convergent rate,which provides a new direction to study the stability of equations.because of this,this article will study the stability of the neutral stochastic differential equations driven by Lévy noises based on the general stability.The main research content of this paper are as follows:(1)In this paper,base on the definitions of almost surely stability and p-moment stability of neutral stochastic functional differential equations with Lévy noise at the general convergent rate,and use It(?) formula,Lyapunov function,stochastic analysis theory and some inequalities,at last the sufficient conditions of these two kinds of stability are obtained.(2)Utilizing the conclusion of(1),we want to analyze the sufficient conditions of these two kinds of stability of the neutral stochastic functional differential equations with time-varying delay driven by Lévy noise.(3)Verify the practicability and effectiveness of the conclusion by the given example.