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Log-Harnack Inequality and Bismut Formula for McKean-Vlasov SDEs with Singularities in all Variables (2207.11536v4)
Published 23 Jul 2022 in math.PR
Abstract: The log-Harnack inequality and Bismut formula are established for McKean-Vlasov SDEs with singularities in all (time, space, distribution) variables, where the drift satisfies an integrability condition in time-space, and the continuity in distribution may be weaker than Dini. The main results considerably improve the existing ones for the case where the drift is $L$-differentiable and Lipschitz continuous in distribution with respect to the 2-Wasserstein distance.