Probability Theory and Related Fields

, Volume 144, Issue 3, pp 581–613

A probabilistic representation of constants in Kesten’s renewal theorem

  • Nathanaël Enriquez
  • Christophe Sabot
  • Olivier Zindy
Article

DOI: 10.1007/s00440-008-0155-9

Cite this article as:
Enriquez, N., Sabot, C. & Zindy, O. Probab. Theory Relat. Fields (2009) 144: 581. doi:10.1007/s00440-008-0155-9
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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.

Keywords

Renewal seriesCouplingFluctuation theory of random walks

Mathematics Subject Classification (2000)

60H2560K05

Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  • Nathanaël Enriquez
    • 1
  • Christophe Sabot
    • 2
  • Olivier Zindy
    • 3
  1. 1.Laboratoire Modal’XUniversité Paris 10NanterreFrance
  2. 2.Institut Camille Jordan, CNRS UMR 5208Université de Lyon, Université Lyon 1Villeurbanne CedexFrance
  3. 3.Weierstrass Institute for Applied Analysis and StochasticsBerlinGermany