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

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• 作者：J.-R. Chazottes and S. Gou?zel
• 关键词：Almost ; sure central limit theorem ; Almost ; sure convergence to stable laws ; Gibbs–Markov map ; Inducing ; Suspension flow ; Martingales ; hyperbolic flow ; Stadium billiard
• 刊名：Probability Theory and Related Fields
• 出版年：2007
• 出版时间：May, 2007
• 年：2007
• 卷：138
• 期：1-2
• 页码：195-234
• 全文大小：437 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematicsr>Probability Theory and Stochastic Processesr>Mathematical and Computational Physicsr>Quantitative Financer>Mathematical Biologyr>Statistics for Business, Economics, Mathematical Finance and Insurancer>Operation Research and Decision Theoryr>
• 出版者：Springer Berlin / Heidelberg
• ISSN：1432-2064

文摘

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.