Bi-Coupling Method and Applications

TL;DR

This paper introduces the bi-coupling argument, a novel technique to estimate relative entropy between diffusion processes, leading to new entropy-cost inequalities with broad applications in stochastic analysis and related fields.

Contribution

The paper develops the bi-coupling argument and applies it to establish entropy-cost inequalities for McKean-Vlasov SDEs with distribution-dependent noise, addressing a long-standing open problem.

Findings

Established entropy-cost inequality for McKean-Vlasov SDEs

Provided a new method for estimating relative entropy between diffusions

Potential applications in optimal transport, information theory, and mean field systems

Abstract

By developing a new technique called the bi-coupling argument, we estimate the relative entropy between different diffusion processes in terms of the distances of initial distributions and drift-diffusion coefficients. As an application, the entropy-cost inequality is established for McKean-Vlasov SDEs with spatial-distribution dependent noise, which is open for a long time and has potential applications in optimal transport, information theory and mean field particle systems.