Roberts, Gareth O.; Rosenthal, Jeffrey S. Geometric ergodicity and hybrid Markov chains. (English) Zbl 0890.60061 Electron. Commun. Probab. 2, 13-25 (1997). 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. Cited in 2 ReviewsCited in 131 Documents MSC: 60J10 Markov chains (discrete-time Markov processes on discrete state spaces) 60J35 Transition functions, generators and resolvents Keywords:Markov chain Monte Carlo; hybrid Monte Carlo; geometric ergodicity; reversibility; spectral gap PDFBibTeX XMLCite \textit{G. O. Roberts} and \textit{J. S. Rosenthal}, Electron. Commun. Probab. 2, 13--25 (1997; Zbl 0890.60061) Full Text: DOI EuDML EMIS