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

2021/07/30 by Wei Hong, Hong, Wei, Shihu Li +3 · 2 citations
Economics, Econometrics and Finance · Engineering · Mathematics · #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Mathematical Biology Tumor Growth #Probability (math.PR) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2107.14401

openalex publication_date 2021/07/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30

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.

Cited by

• Averaging principle for slow-fast systems of PDEs with rough drivers
• Strong averaging principle for nonautonomous multi-scale SPDEs with fully local monotone and almost periodic coefficients

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