Quantitative estimate of the overdamped limit for the Vlasov-Fokker-Planck systems

2021/10/02 by Hui Huang, Huang, Hui
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical Biology Tumor Growth #Probability (math.PR) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2110.00883

openalex publication_date 2021/10/02 · openalex created_date 2021/10/11 · openalex updated_date 2026/07/28

Abstract

This note adapts a probabilistic approach to establish a quantified estimate of the overdamped limit for the Vlasov-Fokker-Planck equation towards the aggregation-diffusion equation, which in particular includes cases of the Newtonian type singular forces. The proofs are based on the investigation of the weak convergence of the corresponding stochastic differential equations (SDEs) of Mckean type in the continuous path space. We show that one can obtain the same convergence rate as in [10] under the same assumptions.

Citations

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