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

TL;DR

This paper investigates the long-term behavior of multivalued McKean-Vlasov stochastic differential equations, proving exponential ergodicity and the convergence of invariant measures under coefficient convergence.

Contribution

It establishes exponential ergodicity and the convergence of invariant measures for multivalued McKean-Vlasov SDEs, extending understanding of their stability and asymptotic properties.

Findings

Proved exponential ergodicity of multivalued McKean-Vlasov SDEs.

Showed convergence of solutions when coefficients converge.

Established convergence of invariant measures based on solution convergence.

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 convergence of corresponding strong solutions are presented. Finally, based on the convergence of these solutions, we establish the convergence of corresponding invariant measures.