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

T. C. Son; D. Q. Le; M. H. Duong

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arXiv · 2209.11967

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

T. C. Son·D. Q. Le·M. H. Duong

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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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BibTeX RIS

T. C. Son, D. Q. Le, M. H. Duong. 2022-09-24. Rate of convergence in the Smoluchowski-Kramers approximation for mean-field stochastic differential equations. https://arxiv.org/abs/2209.11967

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