Rate of homogenization for fully-coupled McKean-Vlasov SDEs

Understand

We consider a fully-coupled slow-fast system of McKean-Vlasov SDEs 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.