Strong Convergence Rates in Averaging Principle for Slow-Fast McKean-Vlasov SPDEs

TL;DR

This paper establishes strong convergence rates for the averaging principle in McKean-Vlasov SPDEs with slow and fast scales, using variational methods and time discretization, applicable to various nonlinear equations.

Contribution

It provides the first rigorous proof of strong convergence rates for averaging in McKean-Vlasov SPDEs with explicit rates, extending classical results to this complex setting.

Findings

Proves strong convergence of slow components to averaged solutions

Derives explicit convergence rates for McKean-Vlasov SPDEs

Applicable to stochastic porous media and p-Laplace equations

Abstract

In this paper, we aim to study the asymptotic behaviour for a class of McKean-Vlasov stochastic partial differential equations with slow and fast time-scales. Using the variational approach and classical Khasminskii time discretization, we show that the slow component strongly converges to the solution of the associated averaged equation. In particular, the corresponding convergence rates are also obtained. The main results can be applied to demonstrate the averaging principle for various McKean-Vlasov nonlinear SPDEs such as stochastic porous media type equation, stochastic $p$-Laplace type equation and also some McKean-Vlasov stochastic differential equations.