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

• 成果类型: Article
• 署名作者: Chazottes, J.-R.; Gouezel, S.
• 署名单位: Institut Polytechnique de Paris; Ecole Polytechnique; Centre National de la Recherche Scientifique (CNRS); Universite de Rennes
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-006-0021-6
• 发表日期: 2007
• 页码: 195-234
• 关键词: decay

摘要

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.