Sharp propagation of chaos for McKean-Vlasov equation with non constant diffusion coefficient

TL;DR

This paper develops a method to achieve precise local propagation of chaos results for particle systems governed by McKean-Vlasov equations with non-constant diffusion coefficients, extending previous work to more general diffusions.

Contribution

It introduces a novel approach using the BBGKY hierarchy to handle non-constant diffusions in propagation of chaos analysis.

Findings

Achieves sharp local propagation of chaos results for non-constant diffusion coefficients.

Extends existing methods to more general diffusion settings.

Uses relative entropy and Fisher information to derive differential inequalities.

Abstract

We present a method to obtain sharp local propagation of chaos results for a system of N particles with a diffusion coefficient that it not constant and may depend of the empirical measure. This extends the recent works of Lacker [14] and Wang [24] to the case of non constant diffusions. The proof relies on the BBGKY hierarchy to obtain a system of differential inequalities on the relative entropy of k particles, involving the fisher information.