Open Access
1997 Geometric Ergodicity and Hybrid Markov Chains
Gareth Roberts, Jeffrey Rosenthal
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Electron. Commun. Probab. 2: 13-25 (1997). DOI: 10.1214/ECP.v2-981


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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Gareth Roberts. Jeffrey Rosenthal. "Geometric Ergodicity and Hybrid Markov Chains." Electron. Commun. Probab. 2 13 - 25, 1997.


Accepted: 14 May 1997; Published: 1997
First available in Project Euclid: 26 January 2016

zbMATH: 0890.60061
MathSciNet: MR1448322
Digital Object Identifier: 10.1214/ECP.v2-981

Primary: 60J25

Keywords: geometric ergodicity , hybrid Monte Carlo , Markov chain Monte Carlo , reversibility , spectral gap

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