Central Limit Theorem Started at a Point for Stationary Processes and Additive Functionals of Reversible Markov Chains

Christophe Cuny () and Magda Peligrad ()
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Christophe Cuny: University of New Caledonia
Magda Peligrad: University of Cincinnati

Journal of Theoretical Probability, 2012, vol. 25, issue 1, 171-188

Abstract: Abstract In this paper we study the almost sure central limit theorem started at a point for additive functionals of a stationary and ergodic Markov chain via a martingale approximation in the almost sure sense. Some of the results provide sufficient conditions for general stationary sequences. We use these results to study the quenched CLT for additive functionals of reversible Markov chains.

Keywords: Quenched central limit theorem; Reversible Markov chains; 60F05; 60F15; 60J05 (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1007/s10959-010-0321-8

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