Exponential ergodicity for singular reflecting McKean–Vlasov SDEs

Abstract

By refining a recent result of Xie and Zhang (2020), we prove the exponential ergodicity under a weighted variation norm for singular SDEs with drift containing a local integrable term and a coercive term. This result is then extended to singular reflecting SDEs as well as singular McKean–Vlasov SDEs with or without reflection. The exponential ergodicity in the relative entropy and (weighted) Wasserstein distances are also studied for reflecting McKean–Vlasov SDEs. The main results are illustrated by non-symmetric singular granular media equations.