Attracting Set And Application Of Delay Stochastic Differential Equations Driven By Related Processes Of Fractional Brownian Motion

In practice,many systems have inevitably delays,that is,the current system change is not only related to the state of the system at the current moment,but also depends on the past state of the system.Moreover,because random factors are ubiquitous in the objective world,many systems not only have delays,but also are more or less disturbed by random factors,which makes it more reasonable to simulate the system with delay stochastic differential equations.Therefore,the use of stochastic analysis technology to study the stability of the solution of delay stochastic differential equation has important theoretical significance and application value.The global attracting set has attracted more and more people to study because it can weaken the stability of stochastic systems.In this paper,attracting set and application of delay stochastic differential equations driven by related processes of fractional Brownian motion is studied.The main research content is as follows:1.We study the global attracting set of a class of impulsive delay stochastic dif-ferential equations driven by tempered fractional Brownian motion^,（）（0<<1/2,>0）.First,we review the knowledge of random integrals of tempered frac-tional Brownian motion and introduce a technical lemma,and then obtain the global attracting set and quasi-invariant set of the considered equations by this technical lemma and the delay integral inequality.In particular,we give sufficient conditions for the-moment exponential decay of the mild solution of the considered equation.2.We study the global attracting set of stochastic differential equations with unbounded delay driven by the fractional Ornstein-Uhlenbeck process(4^,（）（∈（1/2,1））.We review some knowledge about the fractional Ornstein-Uhlenbeck pro-cess.Subsequently,the Banach’s fixed point theorem is used to prove the uniqueness of the mild solution of the considered equation.Finally,the global attracting set of the considered equation is obtained by stochastic analysis,semigroup theory and delay integral inequality.