Almost Sure Central Limit Theorems and the Erdös-Rényi law for Expanding Maps of the Interval

  title={Almost Sure Central Limit Theorems and the Erd{\"o}s-R{\'e}nyi law for Expanding Maps of the Interval},
  author={J.-R. Chazottes},
For a large class of expanding maps of the interval, we prove that partial sums of Lipschitz observables satisfy an almost sure central limit theorem (ASCLT). In fact, we provide a rate of convergence in the Kantorovich distance. Maxima of partial sums are also shown to obey an ASCLT. The key-tool is an exponential inequality recently obtained. Then we establish (optimal) almost-sure convergence rates for the supremum of moving averages of Lipschitz observables (Erdös-Rényi type law). This is… CONTINUE READING

From This Paper

Topics from this paper.


Publications referenced by this paper.
Showing 1-10 of 26 references

On strong versions of the central limit theorem

  • Schatte
  • J . Theor . Probab .
  • 2002

A universal result in almost sure central limit theory , Stochastic Process

  • E. Csáki Berkes
  • 2001

A large deviation principle related to the strong arc - sine law

  • M. Yor Rouault, M. Zani
  • Mathématiques & Applications
  • 2000

Almost sure central limit theorems for strictly stationary processes

  • Liverani
  • Proc . Amer . Math . Soc .
  • 2000

Propriétés statistiques de systèmes dynamiques non markoviens

  • W. Parry Coelho
  • 2000

Fluctuations of repetition times for Gibb - sian sources

  • J.-P. Eckmann Collet
  • Nonlinearity
  • 1999

Asymptotic recurrence and waiting times for stationary processes

  • W. Philipp Lacey
  • J . Theor . Probab .
  • 1998

Specification on the interval

  • A. Galves, B. Schmitt
  • Trans . Amer . Math . Soc .
  • 1997

Similar Papers

Loading similar papers…