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On the central limit theorem for geometrically ergodic Markov chains
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  • Published: 09 October 2004

On the central limit theorem for geometrically ergodic Markov chains

  • Olle Häggström1 

Probability Theory and Related Fields volume 132, pages 74–82 (2005)Cite this article

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Abstract.

Let X0,X1,... be a geometrically ergodic Markov chain with state space and stationary distribution π. It is known that if h:→ R satisfies π(|h|2+ɛ)<∞ for some ɛ>0, then the normalized sums of the X i ’s obey a central limit theorem. Here we show, by means of a counterexample, that the condition π(|h|2+ɛ)<∞ cannot be weakened to only assuming a finite second moment, i.e., π(h2)<∞.

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Authors and Affiliations

  1. Department of Mathematics, Chalmers University of Technology, 412 96, Göteborg, Sweden

    Olle Häggström

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  1. Olle Häggström
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Correspondence to Olle Häggström.

Additional information

Reasearch supported by the Swedish Research Council.

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Cite this article

Häggström, O. On the central limit theorem for geometrically ergodic Markov chains. Probab. Theory Relat. Fields 132, 74–82 (2005). https://doi.org/10.1007/s00440-004-0390-7

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  • Received: 28 April 2004

  • Revised: 30 June 2004

  • Published: 09 October 2004

  • Issue Date: May 2005

  • DOI: https://doi.org/10.1007/s00440-004-0390-7

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Keywords

  • Markov Chain
  • State Space
  • Stochastic Process
  • Probability Theory
  • Limit Theorem
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