Coupling by Change of Measure for Conditional McKean-Vlasov SDEs and Applications

Xing Huang

Published 2023-03-08, updated 2023-05-18Version 2

In this paper, couplings by change of measure are constructed to derive log-Harnack inequalities for conditional McKean-Vlasov SDEs, where the diffusion coefficients corresponding to the common noise are distribution free or merely depend on the distribution variable and for the latter one, the stochastic Hamiltonian system is also considered. Moreover, the quantitative propagation of chaos in Wasserstein distance is obtained, which combined with the coupling by change of measure implies the quantitative propagation of chaos in the relative entropy and total variation distance and in the additive noise case, the initial distributions of interacting particle system and conditional McKean-Vlasov SDEs are allowed to be singular, which is new even in the McKean-Vlasov frame.