Numerical scheme for the invariant measure of highly nonlinear McKean-Vlasov stochastic differential equation

To approximate the invariant measure of McKean-Vlasov stochastic differential equation (MVSDE) with highly nonlinear drift and diffusion coefficients, this paper constructs the backward Euler scheme for the corresponding self-interacting stochastic differential equation (SDE), which depends on both current and historical information. Then the empirical measure of the numerical solution for self-interacting SDE is proved to converge to the invariant measure of the original MVSDE under the Wasserstein distance. The numerical simulations are provided to support this finding.