Variance bounding Markov chains

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

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Probability, 60J10 (Primary) 65C40, 47A10 (Secondary)

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http://salesiana.dossiersoluciones.com/handle/123456789/212799

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0806.2747
 http://arxiv.org/abs/0806.2747
 Annals of Applied Probability 2008, Vol. 18, No. 3, 1201-1214
 doi:10.1214/07-AAP486

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