On Mixing Properties of Reversible Markov Chains

2014/03/19 by Richard C. Bradley, Bradley, Richard C.
Mathematics · #60G10 #60J05 #60J10 #FOS: Mathematics #Probability (math.PR) #math.PR #msc:60G10 #msc:60J05 #msc:60J10

paper · pdf · doi:10.48550/arxiv.1403.4895

17 pages, no figures

arxiv created 2014/03/19 · arxiv updated 2014/03/20

Abstract

It is well known that for a strictly stationary, reversible, Harris recurrent Markov chain, the ρ-mixing condition is equivalent to geometric ergodicity and to a "spectral gap" condition. In this note, it will be shown with an example that for that class of Markov chains, the "interlaced" variant of the ρ-mixing condition fails to be equivalent to those conditions.

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