Strong convergence of propagation of chaos for McKean-Vlasov SDEs with singular interactions

Zimo Hao, Michael Röckner, Xicheng Zhang

Published 2022-04-17Version 1

In this work we show the strong convergence of propagation of chaos for the particle approximation of McKean-Vlasov SDEs with singular $L^p$-interactions as well as the moderate interaction particle system in the level of particle trajectories. One of the main obstacles is to establish the strong well-posedness of particle system with singular interaction. In particular, we develop the theory of strong well-posedness of Krylov and R\"ockner \cite{Kr-Ro} in the case of mixed $L^\bbp$-drifts, where the heat kernel estimates play a crucial role. Moreover, when the interaction kernel is bounded measurable, we also obtain the optimal rate of strong convergence, which is partially based on Jabin and Wang's entropy method \cite{JW16} and Zvonkin's transformation.