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A Conditional CLT which Fails for Ergodic Components

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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.

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Authors and Affiliations

  1. LPA de Beaune Bellegarde, BP 51, 7 rue des deportés, 45340, Beaune la rolande, France

    L. Ouchti

  2. Laboratoire de Mathématiques Raphaël Salem UMR CNRS 6085, Université de Rouen, Avenue de l’Université, 76801, Saint Etienne du Rouvray, France

    D. Volný

Authors
  1. L. Ouchti
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  2. D. Volný
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Correspondence to L. Ouchti.

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Ouchti, L., Volný, D. A Conditional CLT which Fails for Ergodic Components. J Theor Probab 21, 687–703 (2008). https://doi.org/10.1007/s10959-007-0126-6

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  • DOI: https://doi.org/10.1007/s10959-007-0126-6

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