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Geometric ergodicity and hybrid Markov chains. (English) Zbl 0890.60061

Summary: Various notions of geometric ergodicity for Markov chains on general state spaces exist. 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.

MSC:

60J10 Markov chains (discrete-time Markov processes on discrete state spaces)
60J35 Transition functions, generators and resolvents
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