Long Time Propagation of Chaos in Total Variation Distance for Mean Field Interacting Particle System

Xing Huang, Fen-Fen Yang, Chenggui Yuan

Published 2024-04-02Version 1

In this paper, a general result on the long time quantitative propagation of chaos in total variation distance for mean field interacting particle system driven by general L\'{e}vy noise is derived, where the non-interacting drift is assumed to be dissipative in long distance and the initial distribution of interacting particle system converges to that of the limit equation in $L^1$-Wasserstein distance. Moreover, by using the method of coupling, the results are applied to mean field interacting particle system driven by Brownian motion and $\alpha(\alpha>1)$-stable noise respectively.