Rate of Convergence in the Smoluchowski-Kramers Approximation for Mean-field Stochastic Differential Equations

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