On almost-sure versions of classical limit theorems for dynamical systems
Dynamical Systems
2007-05-23 v2 Probability
Abstract
The purpose of this article is to construct a toolbox, in Dynamical Systems, 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.
Cite
@article{arxiv.math/0601388,
title = {On almost-sure versions of classical limit theorems for dynamical systems},
author = {J-R Chazottes and S Gouezel},
journal= {arXiv preprint arXiv:math/0601388},
year = {2007}
}
Comments
41 pages; submitted v2: replaced the argument for Gibbs-Markov maps with a general spectral argument