A Conditional CLT which Fails for Ergodic Components

L. Ouchti () and D. Volný ()
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L. Ouchti: LPA de Beaune Bellegarde
D. Volný: Université de Rouen

Journal of Theoretical Probability, 2008, vol. 21, issue 3, 687-703

Abstract: 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; 60G42; 60F05 (search for similar items in EconPapers)
Date: 2008
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10959-007-0126-6

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