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A stationary, pairwise independent, absolutely regular sequence for which the central limit theorem fails
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  • Published: 01 February 1989

A stationary, pairwise independent, absolutely regular sequence for which the central limit theorem fails

  • Richard C. Bradley1 

Probability Theory and Related Fields volume 81, pages 1–10 (1989)Cite this article

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  • 27 Citations

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Summary

A strictly stationary finite-state non-degenerate random sequence is constructed which satisfies pairwise independence and absolute regularity but fails to satisfy a central limit theorem. The mixing rate for absolute regularity is only slightly slower than that in a corresponding central limit theorem of Ibragimov.

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References

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Author information

Authors and Affiliations

  1. Department of Mathematics, Indiana University, 47405, Bloomington, Indiana, USA

    Richard C. Bradley

Authors
  1. Richard C. Bradley
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Additional information

This work was partially supported by NSF grant DMS 86-00399

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Cite this article

Bradley, R.C. A stationary, pairwise independent, absolutely regular sequence for which the central limit theorem fails. Probab. Th. Rel. Fields 81, 1–10 (1989). https://doi.org/10.1007/BF00343735

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  • Received: 17 March 1987

  • Revised: 22 July 1988

  • Published: 01 February 1989

  • Issue Date: February 1989

  • DOI: https://doi.org/10.1007/BF00343735

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Keywords

  • Markov Chain
  • Limit Theorem
  • Central Limit Theorem
  • Elementary Calculation
  • Stationary Sequence
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