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Which ergodic averages have finite asymptotic variance?

Research output: Contribution to journalArticle

Original languageEnglish
JournalThe Annals of Applied Probability
Accepted/In press27 Sep 2017

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Abstract

We show that the class of L2 functions for which ergodic averages of a reversible Markov chain have finite asymptotic variance is determined by the class of L2 functions for which ergodic averages of its asso- ciated jump chain have finite asymptotic variance. This allows us to characterize completely which ergodic averages have finite asymptotic variance when the Markov chain is an independence sampler. From a practical perspective, the most important result identifies a simple suf- ficient condition for all ergodic averages of L2 functions of the primary variable in a pseudo-marginal Markov chain to have finite asymptotic variance.

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