Averaging principles and central limit theorems for multiscale McKean-Vlasov stochastic systems

TL;DR

This paper investigates multiscale McKean-Vlasov stochastic systems, proving convergence of the slow component to an averaged equation and establishing a central limit theorem for fluctuations.

Contribution

It introduces an averaging principle and a central limit theorem for multiscale McKean-Vlasov systems, with optimal convergence rates.

Findings

Slow component converges to the averaging equation in $L^p$ space with rate 1/2

Established a central limit theorem through tightness arguments

Provides rigorous analysis for multiscale stochastic systems depending on distribution

Abstract

In this paper, we study a class of multiscale McKean-Vlasov stochastic systems where the entire system depends on the distribution of the fast component. First of all, by the Poisson equation method we prove that the slow component converges to the solution of the averaging equation in the $L^p$ ($p\geq 2$) space with the optimal convergence rate 1/2. Then a central limit theorem is established by tightness.