The enhanced Sanov theorem and propagation of chaos

TL;DR

This paper extends Sanov's theorem to interacting Brownian rough paths, providing large deviation principles and propagation of chaos results that facilitate analysis of particle systems and their limits.

Contribution

It introduces a Sanov-type large deviation principle for interacting Brownian rough paths and derives propagation of chaos in rough path spaces.

Findings

Large deviation principles for interacting Brownian rough paths

Propagation of chaos in rough path spaces

Applications to McKean-Vlasov limits

Abstract

We establish a Sanov type large deviation principle for an ensemble of interacting Brownian rough paths. As application a large deviations for the ($k$-layer, enhanced) empirical measure of weakly interacting diffusions is obtained. This in turn implies a propagation of chaos result in rough path spaces and allows for a robust subsequent analysis of the particle system and its McKean-Vlasov type limit, as shown in two corollaries.