Rate of homogenization for fully-coupled McKean-Vlasov SDEs

In this paper, we consider a fully-coupled slow-fast system of McKean-Vlasov stochastic differential equations with full dependence on the slow and fast component and on the law of the slow component and derive convergence rates to its homogenized limit. We do not make periodicity assumptions, but we impose conditions on the fast motion to guarantee ergodicity. In the course of the proof we obtain related ergodic theorems and we gain results on the regularity of Poisson type of equations and of the associated Cauchy problem on the Wasserstein space that are of independent interest.

Automated summary

In this paper, a fully-coupled slow-fast system of McKean-Vlasov stochastic differential equations with full dependence on various components is considered and convergence rates to its homogenized limit are derived. Periodicity assumptions are not made, but conditions on the fast motion are imposed to ensure ergodicity. The proof also yields related ergodic theorems and results on the regularity of Poisson type equations and the associated Cauchy problem on the Wasserstein space which are of independent interest.