Stability Of A Class Of McKean-Vlasov Stochastic Differential Equations

In recent years,due to the gradual maturity and wide application of stochastic differential equation theory and mean field theory,a new class of stochastic differential equations,namely McKean-Vlasov stochastic differential equations,attracts a large number of scholars' attention.They study the well posedness,existence and uniqueness of solutions,ergodicity and so on.On this basis,by using the basic theoretical knowledge of Burkholder-Davis-Gundy inequality,Gronwall inequality and compression mapping theorem,this paper studies a more general stochastic differential equation,The difference between this kind of equation and classical McKean-Vlasov stochastic differential equation is that the drift term and diffusion coefficient are related to the joint distribution of the equation solution and a random variable.Firstly,it is proved that when the drift term b and diffusion coefficient ? meet the first hypothesis,the equation has a unique solution.Secondly,it is proved that the equation has a unique solution when the drift term b and diffusion coefficient ? satisfy the second hypothesis.On this basis,the stability of the solution of the equation with respect to initial value and coefficients is further proved.