Quantitative Contraction Rates for McKean-Vlasov Stochastic Differential Equations with Multiplicative Noise

TL;DR

This paper establishes explicit contraction rates for McKean-Vlasov SDEs with multiplicative noise, demonstrating uniform propagation of chaos and exponential ergodicity under certain conditions.

Contribution

It provides the first explicit quantitative contraction rates for these SDEs, advancing understanding of their long-term behavior and particle system convergence.

Findings

Derived explicit contraction rates in Wasserstein distances.

Proved uniform propagation of chaos over time.

Established exponential ergodicity for McKean-Vlasov SDEs.

Abstract

This work focuses on the quantitative contraction rates for McKean-Vlasov stochastic differential equations (SDEs) with multiplicative noise. Under suitable conditions on the coefficients of the SDE, this paper derives explicit quantitative contraction rates for the convergence in Wasserstein distances of McKean-Vlasov SDEs using the coupling method.The contraction results are then used to prove a propagation of chaos uniformly in time, which provides quantitative bounds on convergence rate of interacting particle systems, and establishes exponential ergodicity for McKean-Vlasov SDEs.