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Central limit theorem for triangular arrays of non-homogeneous Markov chains
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  • Published: 03 June 2011

Central limit theorem for triangular arrays of non-homogeneous Markov chains

  • Magda Peligrad1 

Probability Theory and Related Fields volume 154, pages 409–428 (2012)Cite this article

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Abstract

In this paper we obtain the central limit theorem for triangular arrays of non-homogeneous Markov chains under a condition imposed to the maximal coefficient of correlation. The proofs are based on martingale techniques and a sharp lower bound estimate for the variance of partial sums. The results complement an important central limit theorem of Dobrushin based on the contraction coefficient.

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Authors and Affiliations

  1. Department of Mathematical Sciences, University of Cincinnati, PO Box 210025, Cincinnati, OH, 45221-0025, USA

    Magda Peligrad

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  1. Magda Peligrad
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Corresponding author

Correspondence to Magda Peligrad.

Additional information

Supported in part by a Charles Phelps Taft Memorial Fund grant, NSF DMS-0830579 and NSA grants H98230-09-1-0005 and H98230-11-1-0135.

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Cite this article

Peligrad, M. Central limit theorem for triangular arrays of non-homogeneous Markov chains. Probab. Theory Relat. Fields 154, 409–428 (2012). https://doi.org/10.1007/s00440-011-0371-6

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  • Received: 01 December 2010

  • Revised: 13 May 2011

  • Published: 03 June 2011

  • Issue Date: December 2012

  • DOI: https://doi.org/10.1007/s00440-011-0371-6

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Keywords

  • Central limit theorem
  • Triangular arrays
  • Non-homogeneous Markov chains
  • Maximal coefficient of correlation

Mathematics Subject Classification (2000)

  • Primary 60F05
  • 60J10
  • 60G48
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