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A Conditional CLT which Fails for Ergodic Components

Author

Listed:
  • L. Ouchti

    (LPA de Beaune Bellegarde)

  • D. Volný

    (Université de Rouen)

Abstract

We show that the conditional central limit theorem can take place for a stationary process defined on a nonergodic dynamical system while this last does not satisfy the central limit theorem for any ergodic component. There exists an ergodic Markov chain such that the conditional central limit theorem is satisfied for an invariant measure but fails to hold for almost all starting points.

Suggested Citation

  • L. Ouchti & D. Volný, 2008. "A Conditional CLT which Fails for Ergodic Components," Journal of Theoretical Probability, Springer, vol. 21(3), pages 687-703, September.
    • Handle: RePEc:spr:jotpro:v:21:y:2008:i:3:d:10.1007_s10959-007-0126-6
    DOI: 10.1007/s10959-007-0126-6
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    References listed on IDEAS

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    1. Woodroofe, Michael, 1992. "A central limit theorem for functions of a Markov chain with applications to shifts," Stochastic Processes and their Applications, Elsevier, vol. 41(1), pages 33-44, May.
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    Cited by:

    1. 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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