A Route to Harris ergodicity for Non-Feller Markov Kernels

Abstract

For non-Feller Markov kernels satisfying a quasi-Feller factorization, the compact-petite-set criterion gives petite compact sets under \(\psi\)-irreducibility when the support of \(\psi\) has non-empty interior. Thus, for coercive Lyapunov functions, the sublevel sets used in the Harris--Lyapunov argument are petite. Under aperiodicity they are small. The Hairer--Mattingly contraction theorem then yields geometric ergodicity in weighted total variation under the usual geometric drift condition.