Special Session 36: Stochastic Systems, SDEs/SPDEs, Games, Quantum-Computing and Storages

Quantitative Contraction Rates for McKean-Vlasov Stochastic Differential Equationswith Multiplicative Noise

Chao Zhu
University of Wisconsin-Milwaukee
This work focuses on the quantitative contraction rates for McKean-Vlasov stochastic differential equations (SDEs) with multiplicative noises. Under suitable conditions on the coefficients of the SDE, we derive 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.