Asymptotic strong Feller property and local weak irreducibility via generalized couplings

Oleg Butkovsky, Fabrice Wunderlich

Published 2019-12-12Version 1

In this short note we show how the asymptotic strong Feller property (ASF) and local weak irreducibility can be established via generalized couplings. We also prove that a stronger form of ASF together with local weak irreducibility implies uniqueness of an invariant measure. The latter result is optimal in a certain sense and complements some of the corresponding results of Hairer, Mattingly (2008).