Almost Sure Central Limit Theorems and the Erdos-Renyi law for Expanding Maps of the Interval

Thumbnail Image

Date

Authors

Journal Title

Journal ISSN

Volume Title

Publisher

Abstract

Description

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 speed of convergence in the Kantorovich metric. Maxima of partial sums are also shown to obey an ASCLT. The key-tool is an exponential inequality recently obtained. Then we derive almost-sure convergence rates for the supremum of moving averages of Lipschitz observables (Erdos-Renyi type law). We end up with an application to entropy estimation ASCLT's that refi ne Shannon-McMillan-Breiman and Ornstein-Weiss theorems.
25p; title has changed; minor corrections; published in Erg. Th. Dynam. Sys. (2005)

Keywords

Probability, Dynamical Systems

Citation

URI

http://salesiana.dossiersoluciones.com/handle/123456789/160976

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0210286
 http://arxiv.org/abs/math/0210286

Collections

arXiv