Strong Convergence of Propagation of Chaos for McKean–Vlasov SDEs with Singular Interactions

Abstract

Abstract. In this work we show the strong convergence of propagation of chaos for the particle approximation of McKean-Vlasov SDEs with singular [Formula: see text]-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 Röckner [ Probab. Theory Related Fields, 131 (2005), pp. 154–196] to the case of mixed [Formula: see text]-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.

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