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Quenched Invariance Principles via Martingale Approximation

  • Magda PeligradEmail author
Chapter
Part of the Fields Institute Communications book series (FIC, volume 76)

Abstract

In this paper we survey the almost sure central limit theorem and its functional form (quenched) for stationary and ergodic processes. For additive functionals of a stationary and ergodic Markov chain these theorems are known under the terminology of central limit theorem and its functional form, started at a point. All these results have in common that they are obtained via a martingale approximation in the almost sure sense. We point out several applications of these results to classes of mixing sequences, shift processes, reversible Markov chains, Metropolis Hastings algorithms.

Keywords

Markov Chain Central Limit Theorem Stationary Sequence Invariance Principle Markov Operator 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgements

The author would like to thank the referees for carefully reading the manuscript and for many useful suggestions that improved the presentation of this paper. This paper was Ssupported in part by a Charles Phelps Taft Memorial Fund grant, the NSA grant H98230-11-1-0135 and the NSF grant DMS-1208237.

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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Department of Mathematical SciencesUniversity of CincinnatiCincinnatiUSA

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