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

Author

Listed:
  • Christophe Cuny

    (University of New Caledonia)

  • Magda Peligrad

    (University of Cincinnati)

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.

Suggested Citation

  • Christophe Cuny & Magda Peligrad, 2012. "Central Limit Theorem Started at a Point for Stationary Processes and Additive Functionals of Reversible Markov Chains," Journal of Theoretical Probability, Springer, vol. 25(1), pages 171-188, March.
    • Handle: RePEc:spr:jotpro:v:25:y:2012:i:1:d:10.1007_s10959-010-0321-8
    DOI: 10.1007/s10959-010-0321-8
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    Cited by:

    1. Na Zhang & Lucas Reding & Magda Peligrad, 2020. "On the Quenched Central Limit Theorem for Stationary Random Fields Under Projective Criteria," Journal of Theoretical Probability, Springer, vol. 33(4), pages 2351-2379, December.
    2. Magda Peligrad & Dalibor Volný, 2020. "Quenched Invariance Principles for Orthomartingale-Like Sequences," Journal of Theoretical Probability, Springer, vol. 33(3), pages 1238-1265, September.

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