Rate of convergence in the Smoluchowski-Kramers approximation for mean-field stochastic differential equations

2022/09/24 by T. C. Son, Son, T. C., Dai-Nam Le +3
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2209.11967

openalex publication_date 2022/09/24 · openalex created_date 2022/09/28 · openalex updated_date 2026/07/28

Abstract

In this paper we study a second-order mean-field stochastic differential systems describing the movement of a particle under the influence of a time-dependent force, a friction, a mean-field interaction and a space and time-dependent stochastic noise. Using techniques from Malliavin calculus, we establish explicit rates of convergence in the zero-mass limit (Smoluchowski-Kramers approximation) in the L^p-distances and in the total variation distance for the position process, the velocity process and a re-scaled velocity process to their corresponding limiting processes.

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