Homogenization of conditional slow-fast McKean-Vlasov SDEs

Abstract: We study a fully-coupled system of conditional slow-fast McKean-Vlasov Stochastic Differential Equations that exhibit full dependence on both the slow and fast components, as well as on the conditional law of the slow component. Our aim is to derive convergence rates to its homogenized limit, without making periodicity assumptions. To prove our results, we utilize a perturbation method for equations posed in the Wasserstein space.