Various notions of geometric ergodicity for Markov chains on general state spaces exist. In this paper, we review certain relations and implications among them. We then apply these results to a collection of chains commonly used in Markov chain Monte Carlo simulation algorithms, the so-called hybrid chains. We prove that under certain conditions, a hybrid chain will "inherit" the geometric ergodicity of its constituent parts.
"Geometric Ergodicity and Hybrid Markov Chains." Electron. Commun. Probab. 2 13 - 25, 1997. https://doi.org/10.1214/ECP.v2-981