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A Bernstein type inequality and moderate deviations for weakly dependent sequences
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  • Published: 09 June 2010

A Bernstein type inequality and moderate deviations for weakly dependent sequences

  • Florence Merlevède1,
  • Magda Peligrad2 &
  • Emmanuel Rio3 

Probability Theory and Related Fields volume 151, pages 435–474 (2011)Cite this article

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Abstract

In this paper we present a Bernstein-type tail inequality for the maximum of partial sums of a weakly dependent sequence of random variables that is not necessarily bounded. The class considered includes geometrically and subgeometrically strongly mixing sequences. The result is then used to derive asymptotic moderate deviation results. Applications are given for classes of Markov chains, iterated Lipschitz models and functions of linear processes with absolutely regular innovations.

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Author information

Authors and Affiliations

  1. Laboratoire de mathématiques, Université Paris Est, UMR 8050 CNRS, Bâtiment Copernic, 5 Boulevard Descartes, 77435, Champs-Sur-Marne, France

    Florence Merlevède

  2. Department of Mathematical Sciences, University of Cincinnati, P.O. Box 210025, Cincinnati, OH, 45221-0025, USA

    Magda Peligrad

  3. Laboratoire de mathématiques, Université de Versailles, UMR 8100 CNRS, Bâtiment Fermat, 45 Avenue des Etats-Unis, 78035, Versailles, France

    Emmanuel Rio

Authors
  1. Florence Merlevède
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  2. Magda Peligrad
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  3. Emmanuel Rio
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Corresponding author

Correspondence to Emmanuel Rio.

Additional information

M. Peligrad is supported in part by a Charles Phelps Taft Memorial Fund grant, and NSA grants, H98230-07-1-0016 and H98230-09-1-0005. E. Rio is supported in part by Centre INRIA Bordeaux Sud-Ouest & Institut de Mathématiques de Bordeaux.

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Merlevède, F., Peligrad, M. & Rio, E. A Bernstein type inequality and moderate deviations for weakly dependent sequences. Probab. Theory Relat. Fields 151, 435–474 (2011). https://doi.org/10.1007/s00440-010-0304-9

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  • Received: 29 January 2009

  • Revised: 07 May 2010

  • Published: 09 June 2010

  • Issue Date: December 2011

  • DOI: https://doi.org/10.1007/s00440-010-0304-9

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Keywords

  • Deviation inequality
  • Moderate deviations principle
  • Semiexponential tails
  • Weakly dependent sequences
  • Strong mixing
  • Absolute regularity
  • Linear processes

Mathematics Subject Classification (2000)

  • 60E15
  • 60F10
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