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.
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M. Peligrad’s research was supported in part by a Charles Phelps Taft Memorial Fund grant and NSA grant H98230-09-1-0005.
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Cuny, C., Peligrad, M. Central Limit Theorem Started at a Point for Stationary Processes and Additive Functionals of Reversible Markov Chains. J Theor Probab 25, 171–188 (2012). https://doi.org/10.1007/s10959-010-0321-8
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DOI: https://doi.org/10.1007/s10959-010-0321-8