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A probabilistic representation of constants in Kesten’s renewal theorem
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  • Published: 07 May 2008

A probabilistic representation of constants in Kesten’s renewal theorem

  • Nathanaël Enriquez1,
  • Christophe Sabot2 &
  • Olivier Zindy3 

Probability Theory and Related Fields volume 144, pages 581–613 (2009)Cite this article

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  • 26 Citations

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Abstract

The aims of this paper are twofold. Firstly, we derive a probabilistic representation for the constant which appears in the one-dimensional case of Kesten’s renewal theorem. Secondly, we estimate the tail of a related random variable which plays an essential role in the description of the stable limit law of one-dimensional transient sub-ballistic random walks in random environment.

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Author information

Authors and Affiliations

  1. Laboratoire Modal’X, Université Paris 10, 200 Avenue de la République, 92001, Nanterre, France

    Nathanaël Enriquez

  2. Institut Camille Jordan, CNRS UMR 5208, Université de Lyon, Université Lyon 1, 43, Boulevard du, 69622, Villeurbanne Cedex, France

    Christophe Sabot

  3. Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstrasse 39, 10117, Berlin, Germany

    Olivier Zindy

Authors
  1. Nathanaël Enriquez
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  2. Christophe Sabot
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  3. Olivier Zindy
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Corresponding author

Correspondence to Nathanaël Enriquez.

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Enriquez, N., Sabot, C. & Zindy, O. A probabilistic representation of constants in Kesten’s renewal theorem. Probab. Theory Relat. Fields 144, 581–613 (2009). https://doi.org/10.1007/s00440-008-0155-9

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  • Received: 16 May 2007

  • Revised: 13 March 2008

  • Published: 07 May 2008

  • Issue Date: July 2009

  • DOI: https://doi.org/10.1007/s00440-008-0155-9

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Keywords

  • Renewal series
  • Coupling
  • Fluctuation theory of random walks

Mathematics Subject Classification (2000)

  • 60H25
  • 60K05
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