Propagation of Chaos for Mean Field Interacting Particle System with Multiplicative Noise

Xing Huang

Published 2023-08-29Version 1

In this paper, the quantitative propagation of chaos for mean field interacting particle system with multiplicative noise in relative entropy is obtained, where the diffusion is distribution free, the interaction in the drift is bounded or Lipschitz continuous and the initial distribution of interacting particles is allowed to be singular with that of the limit equation. When the interaction in both the diffusion and drift is Lipschitz continuous, the quantitative propagation of chaos in $L^\eta$($\eta\in(0,1)$)-Wasserstein distance is proved, which seems to be the first result on quantitative propagation of chaos in $L^\eta$($\eta\in(0,1)$)-Wasserstein distance in the literature. Furthermore, the long time quantitative propagation of chaos in relative entropy as well as $L^2$(-Wasserstein distance is also derived under dissipative condition.