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Journal of Theoretical Probability

, Volume 21, Issue 3, pp 687–703 | Cite as

A Conditional CLT which Fails for Ergodic Components

  • L. Ouchti
  • D. Volný
Article

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.

Keywords

Central limit theorem Martingale Ergodic measure Ergodic component Annealed CLT Quenched CLT Markov chain 

Mathematics Subject Classification (2000)

60G42 60F05 

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Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.LPA de Beaune BellegardeBeaune la rolandeFrance
  2. 2.Laboratoire de Mathématiques Raphaël Salem UMR CNRS 6085Université de RouenSaint Etienne du RouvrayFrance

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