McKean-Vlasov equations with rough common noise

TL;DR

This paper establishes well-posedness for McKean-Vlasov equations driven by rough common noise, extending the theory to equations with measurable coefficients using rough path techniques.

Contribution

It introduces a framework for analyzing McKean-Vlasov equations with rough noise and measurable coefficients, advancing the mathematical understanding of such stochastic systems.

Findings

Proved well-posedness under natural regularity assumptions

Extended rough path theory to McKean-Vlasov equations

Validated the approach with rigorous mathematical results

Abstract

We show well-posedness for McKean--Vlasov equations with rough common noise and progressively measurable coefficients. Our results are valid under natural regularity assumptions on the coefficients, in agreement with the respective requirements of Ito and rough path theory. To achieve these goals, we work in the framework of rough stochastic differential equations recently developed by the authors of this article.