A VECTOR-VALUED ALMOST SURE INVARIANCE PRINCIPLE FOR HYPERBOLIC DYNAMICAL SYSTEMS

被引：62

作者：

Melbourne, Ian ^{[1
]}

Nicol, Matthew ^{[2
]}

机构：

[1] Univ Surrey, Dept Math & Stat, Guildford GU2 7XH, Surrey, England

[2] Univ Houston, Dept Math, Houston, TX 77204 USA

来源：

ANNALS OF PROBABILITY | 2009年 / 37卷 / 02期

基金：

英国工程与自然科学研究理事会;

关键词：

Almost sure invariance principle; nonuniform hyperbolicity; Lorentz gases; Brownian motion; Young towers; CENTRAL LIMIT-THEOREMS; STATISTICAL PROPERTIES; RANDOM-VARIABLES; MARTINGALES; FLOWS; DECAY; APPROXIMATION; RECURRENCE; SEQUENCES; BILLIARDS;

D O I：

10.1214/08-AOP410

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We prove an almost sure invariance principle (approximation by d-dimensional Brownian motion) for vector-valued Holder observables of large classes of nonuniformly hyperbolic dynamical systems. These systems include Axiom A diffeomorphisms and flows as well as systems modeled by Young towers with moderate tail decay rates. In particular, the position variable of the planar periodic Lorentz gas with finite horizon approximates a two-dimensional Brownian motion.

引用

页码：478 / 505

页数：28

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