Probability distance estimates between diffusion processes and applications to singular McKean-Vlasov SDEs

The Lk-Wasserstein distance Wk(k >= 1) and the probability distance W psi induced by a concave function psi, are estimated between different diffusion processes with singular coefficients. As applications, the wellposedness, probability distance estimates and the log-Harnack inequality are derived for McKean-Vlasov SDEs with multiplicative distribution dependent noise, where the coefficients are singular in time-space variables and (Wk + W psi)-Lipschitz continuous in the distribution variable. This improves existing results derived in the literature under the Wk-Lipschitz or derivative conditions in the distribution variable. (c) 2024 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.