PUB - Publikationen an der Universität Bielefeld

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 for the moderate interaction particle systems on the level of particle trajectories. One of the main obstacles is to establish the strong well-posedness of the SDEs for particle systems with singular interaction. To this end, we extend the results on strong well-posedness of Krylov and Rockner [Probab. Theory Related Fields, 131 (2005), pp. 154--196] to the case of mixed L-p-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 [P. -E. Jabin and Z. Wang, J. Funct. Anal., 271 (2016), pp. 3588--3627] and Zvonkin's transformation.