Quantitative Propagation of Chaos in $L^\eta(\eta\in(0,1])$-Wasserstein distance for Mean Field Interacting Particle System

TL;DR

This paper establishes quantitative bounds on the propagation of chaos in $L^ta$-Wasserstein distance for mean field particle systems, accommodating interacting diffusion coefficients and initial distributions converging in $L^1$-Wasserstein distance.

Contribution

It extends propagation of chaos results to $L^ta$-Wasserstein distances with interacting diffusions and initial data convergence in $L^1$-Wasserstein, using gradient estimates of decoupled SDEs.

Findings

Derived quantitative propagation of chaos bounds in $L^ta$-Wasserstein distance.

Analyzed non-degenerate and second order systems separately.

Utilized gradient estimates of decoupled SDEs as main analytical tool.

Abstract

In this paper, quantitative propagation of chaos in $L^\eta$($\eta\in(0,1]$)-Wasserstein distance for mean field interacting particle system is derived, where the diffusion coefficient is allowed to be interacting and the initial distribution of interacting particle system converges to that of the limit equation in $L^1$-Wasserstein distance. The non-degenerate and second order system are investigated respectively and the main tool relies on the gradient estimate of the decoupled SDEs.