Efficient Numerical Approximation of Invariant Probability Measures for McKean-Vlasov Stochastic Differential Equations

This paper establishes the convergence rate of the weighted empirical measure of a self-interacting process to the invariant probability measure of McKean-Vlasov stochastic differential equations (MV-SDEs). It then designs an Euler-Maruyama (EM) scheme for the self-interacting process and derives the convergence rate between the weighted empirical measure of the EM numerical solution and the invariant measure of MV-SDEs.