Log-Harnack Inequality and Bismut Formula for McKean-Vlasov SDEs with Singularities in all Variables
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.
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