On Mixing Properties of Reversible Markov Chains

Abstract

It is well known that for a strictly stationary, reversible, Harris recurrent Markov chain, the $\rho$-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 $\rho$-mixing condition fails to be equivalent to those conditions.

17 pages, no figures

References in corpus (1)

• Some Aspects of Modeling Dependence in Copula-based Markov chains

Cited by in corpus (2)

• An exposition of some basic features of strictly stationary, reversible Markov chains
• A "cousin" of a theorem of Csáki and Fischer