Variance bounding Markov chains

Details Variance bounding Markov chains Variance bounding Markov chains

2008-06-17

arxiv.org/abs/0806.2747v1

Annals of Applied Probability 2008, Vol. 18, No. 3, 1201-1214

Mathematics

Probability

Published in at http://dx.doi.org/10.1214/07-AAP486 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Inst

Scientific paper

10.1214/07-AAP486

We introduce a new property of Markov chains, called variance bounding. We prove that, for reversible chains at least, variance bounding is weaker than, but closely related to, geometric ergodicity. Furthermore, variance bounding is equivalent to the existence of usual central limit theorems for all $L^2$ functionals. Also, variance bounding (unlike geometric ergodicity) is preserved under the Peskun order. We close with some applications to Metropolis--Hastings algorithms.

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