Quantitative propagation of chaos for particle systems with bounded kernels and multiplicative noise

TL;DR

This paper establishes quantitative propagation of chaos for stochastic particle systems with bounded interaction kernels and multiplicative noise, extending existing entropy-based methods to handle diffusion errors.

Contribution

It extends the entropy framework to include multiplicative noise, providing new quantitative propagation of chaos results without requiring Lipschitz or smoothness conditions.

Findings

Proves propagation of chaos for systems with bounded kernels and multiplicative noise.

Extends exponential laws of large numbers to diffusion kernels.

Develops a dynamic combinatorial analysis for error control.

Abstract

We prove the quantitative propagation of chaos for stochastic particle systems with interaction in both the drift and the diffusion coefficients, provided the drift kernel is bounded and free of Lipschitz or smoothness assumptions. Our proof is based on the relative entropy framework of Jabin and Wang \cite{JW2018}, and applies and extends their work on the exponential laws of large numbers. We extend one of their exponential laws of large numbers from the drift to the diffusion kernel to handle the error term arising from multiplicative noise in the entropy evolution equation. Proving this extension relies on a dynamic combinatorial analysis.