Regularity and propagation of chaos for conditional McKean-Vlasov equations

TL;DR

This paper investigates the propagation of chaos in conditional McKean-Vlasov equations, employing nonparametric estimators and entropy methods to establish convergence rates under regularity conditions.

Contribution

It introduces a novel approach combining Nadaraya--Watson estimators with entropy techniques to analyze propagation of chaos for conditional McKean-Vlasov equations.

Findings

Established convergence rates for propagation of chaos

Developed a bootstrap argument for density regularity

Integrated nonparametric estimation with entropy methods

Abstract

We study the rate of propagation of chaos for a McKean--Vlasov equation with conditional expectation terms in the drift. We use a (regularized) Nadaraya--Watson estimator at a particle level to approximate the conditional expectations; we then combine relative entropy methods in the spirit of Jabin and Wang (2018) with information theoretic inequalities to obtain the result. The nonparametric nature of the problem requires higher regularity for the density of the McKean--Vlasov limit, which we obtain with a bootstrap argument and energy estimates.