Homogenization of conditional slow-fast McKean-Vlasov SDEs

TL;DR

This paper investigates the homogenization of complex coupled slow-fast McKean-Vlasov SDEs with full dependence on components and their conditional laws, establishing convergence rates without relying on periodicity assumptions.

Contribution

It introduces a perturbation method in Wasserstein space to derive convergence rates for fully coupled conditional McKean-Vlasov SDEs without periodicity.

Findings

Established convergence rates to the homogenized limit.

Developed a perturbation approach in Wasserstein space.

Extended homogenization theory to fully coupled McKean-Vlasov systems.

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.