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On almost-sure versions of classical limit theorems for dynamical systems
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  • Published: 01 August 2006

On almost-sure versions of classical limit theorems for dynamical systems

  • J.-R. Chazottes1 &
  • S. Gouëzel2 

Probability Theory and Related Fields volume 138, pages 195–234 (2007)Cite this article

Abstract

The purpose of this article is to support the idea that “whenever we can prove a limit theorem in the classical sense for a dynamical system, we can prove a suitable almost-sure version based on an empirical measure with log-average”. We follow three different approaches: martingale methods, spectral methods and induction arguments. Our results apply, among others, to Axiom A maps or flows, to systems inducing a Gibbs–Markov map, and to the stadium billiard.

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Author information

Authors and Affiliations

  1. CPhT, CNRS-Ecole Polytechnique, 91128, Palaiseau Cedex, France

    J.-R. Chazottes

  2. IRMAR, Université de Rennes 1, Campus de Beaulieu, 35042, Rennes Cedex, France

    S. Gouëzel

Authors
  1. J.-R. Chazottes
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  2. S. Gouëzel
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Correspondence to J.-R. Chazottes.

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Chazottes, JR., Gouëzel, S. On almost-sure versions of classical limit theorems for dynamical systems. Probab. Theory Relat. Fields 138, 195–234 (2007). https://doi.org/10.1007/s00440-006-0021-6

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  • Received: 16 January 2006

  • Revised: 01 June 2006

  • Published: 01 August 2006

  • Issue Date: May 2007

  • DOI: https://doi.org/10.1007/s00440-006-0021-6

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Keywords

  • Almost-sure central limit theorem
  • Almost-sure convergence to stable laws
  • Gibbs–Markov map
  • Inducing
  • Suspension flow
  • Martingales
  • hyperbolic flow
  • Stadium billiard
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