Uniform in Time Propagation of Chaos for Mean Field Particle System with Interacting Noise and Partially Dissipative Drifts

TL;DR

This paper establishes uniform in time propagation of chaos for mean field particle systems with interacting noise and partially dissipative drifts, using reflection coupling and gradient estimates.

Contribution

It introduces a novel approach to prove uniform propagation of chaos in Wasserstein distance for systems with interacting noise and partial dissipation.

Findings

Proves uniform propagation of chaos in $L^1$-Wasserstein distance.

Employs reflection coupling and gradient estimates.

Handles systems with interacting diffusion coefficients.

Abstract

In this paper, uniform in time quantitative propagation of chaos in $L^1$-Wasserstein distance for mean field interacting particle system is derived, where the diffusion coefficient is allowed to be interacting and the drift is assumed to be partially dissipative. The main tool relies on reflection coupling, the gradient estimate of the decoupled SDEs, and the Duhamel formula for two semigroups associated to two time-inhomogeneous diffusion processes on $(\R^d)^N$.