Geometric Ergodicity and Hybrid Markov Chains
Gareth O. Roberts, University of Cambridge
Jeffrey S. Rosenthal, University of Toronto
Abstract
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.
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