Invariant Probability Measure for McKean-Vlasov SDEs with Singular Drifts

Xing Huang, Shen Wang, Fen-Fen Yang

Published 2021-08-12Version 1

In this paper, utilizing Wang's Harnack inequality with power and the Banach fixed point theorem, the weak well-posedness for distribution dependent SDEs with integrable drift is investigated. In addition, using a trick of decoupled method, some regularity such as relative entropy and Sobolev's estimate of invariant probability measure are proved. Furthermore, by comparing two stationary Fokker-Planck-Kolmogorov equations, the existence and uniqueness of invariant probability measure for McKean-Vlasov SDEs are obtained by log-Sobolev's inequality and Banach's fixed theorem. Finally, some examples are presented.