  This paper proves that, under a monotonicity condition, the invariant
probability measure of a McKean--Vlasov process can be approximated by weighted
empirical measures of some processes including itself. These processes are
described by distribution dependent or empirical measure dependent stochastic
differential equations constructed from the equation for the McKean--Vlasov
process. Convergence of empirical measures is characterized by upper bound
estimates for their Wasserstein distance to the invariant measure. The
theoretical results are demonstrated via a mean-field Ornstein--Uhlenbeck
process.
