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

Ta Cong Son, Dung Quang Le, Manh Hong Duong*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

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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 Lp-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.
Original languageEnglish
JournalPotential Analysis
Early online date3 Jul 2023
DOIs
Publication statusE-pub ahead of print - 3 Jul 2023

Keywords

  • Smoluchowski-Kramers approximation
  • Stochastic differential by mean-field
  • Total variation distance
  • Malliavin calculus

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