Electronic Communications in Probability

Geometric Ergodicity and Hybrid Markov Chains

Gareth Roberts and Jeffrey Rosenthal

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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.

Article information

Electron. Commun. Probab., Volume 2 (1997), paper no. 2, 13-25.

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60J25: Continuous-time Markov processes on general state spaces

Markov chain Monte Carlo hybrid Monte Carlo geometric ergodicity reversibility spectral gap

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Roberts, Gareth; Rosenthal, Jeffrey. Geometric Ergodicity and Hybrid Markov Chains. Electron. Commun. Probab. 2 (1997), paper no. 2, 13--25. doi:10.1214/ECP.v2-981. https://projecteuclid.org/euclid.ecp/1453832497

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