Stability Analysis Of Stochastic Functional Differential Equations With Infinite Delay And Poisson Jumps

Stochastic differential equations have been applied to many fields such as scientific research and finance.But in reality,many systems are affected not only by time delays,but also by interval or sudden random factors.When these factors cannot be ignored,the traditional stochastic differential equations can not fit such systems well.So,stochastic functional differential equations with Poisson jumps are introduced.At present,the study of such equations has received much attention.However,for such stochastic functional differential equations with Poisson jump,most people consider the limited time delay.but it is not applicable for some special cases,such as climate change or changes in some biological population systems caused by human activities,it often takes decades or even hundreds of years to emerge.In order to accurately describe this phenomenon,people have built a random functional differential equation model with infinite time delay and Poisson jump.Obviously,the study of such equations is also of important theoretical significance and practical value.Therefore,this paper will study the stability of stochastic functional differential equations with infinite delays and Poisson jumps.The main results of this paper are as follows:(1)Literature data on the stability of stochastic differential equations with infinite time delay and Poisson-jump are summarized,collated and analyzed.The present research development status and existing problems are introduced.(2)We discuss the pth moment stochastic stability,the pth moment uniform stochastic stability,the pth moment asymptotically stability of the stochastic functional differential equations with infinite delays and Poisson jumps and obtain the sufficient conditions for these three kinds of stability.(3)We construct a Dini differential inequality with infinite delay and discuss the exponential stability and almost necessarily exponential stability of stochastic functional differential equations with infinite delay and Poisson jumps based on the inequality,Lyapunov function method and It(?) formula,and finally give sufficient conditions for these two types of stability.(4)Based on the adequacy conditions of(2)and(3),the stability of stochastic differential equations with Poisson jump and distributed delay is studied,and the validity and practicability of the results are illustrated by numerical examples.