Limit theorems of invariant measures for multivalued McKean-Vlasov stochastic differential equations

Abstract

The work concerns invariant measures for multivalued McKean-Vlasov stochastic differential equations. First of all, we prove the exponential ergodicity of these equations. Then for a sequence of these equations, when their coefficients converge in the suitable sense, the strong convergence of corresponding strong solutions are presented. Finally, based on the convergence of these solutions, we establish the convergence of corresponding invariant measures with respect to the 1-Wasserstein distance.