Electronic Communications in Probability

Geometric Ergodicity and Hybrid Markov Chains

Gareth Roberts and Jeffrey Rosenthal

Full-text: Open access

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.

Article information

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

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

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1453832497

Digital Object Identifier
doi:10.1214/ECP.v2-981

Mathematical Reviews number (MathSciNet)
MR1448322

Zentralblatt MATH identifier
0890.60061

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

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

Rights
This work is licensed under a Creative Commons Attribution 3.0 License.

Citation

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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