Sequential propagation of chaos

TL;DR

This paper introduces a new sequential particle system to approximate McKean-Vlasov processes, proving convergence and propagation of chaos with quantitative estimates, supported by numerical experiments.

Contribution

It proposes a novel class of sequentially interacting particle systems and establishes their convergence to McKean-Vlasov processes with quantitative propagation of chaos results.

Findings

Weighted empirical measures converge to the McKean-Vlasov law

Quantitative propagation of chaos estimates are provided

Numerical experiments confirm theoretical results

Abstract

A new class of particle systems with sequential interaction is proposed to approximate the McKean-Vlasov process that originally arises as the limit of the mean-field interacting particle system. The weighted empirical measure of this particle system is proved to converge to the law of the McKean-Vlasov process as the system grows. Based on the Wasserstein metric, quantitative propagation of chaos results are obtained for two cases: the finite time estimates under the monotonicity condition and the uniform in time estimates under the dissipation and the non-degenerate conditions. Numerical experiments are implemented to demonstrate the theoretical results.