Rates in almost sure invariance principle for quickly mixing dynamical systems

被引：11

作者：

Cuny, C. ^{[1
]}

Dedecker, J. ^{[2
]}

Korepanov, A. ^{[3
]}

Merlevede, F. ^{[4
]}

机构：

[1] Univ Brest, LMBA, UMR 6205, CNRS, Brest, France

[2] Univ Paris 05, Sorbonne Paris Cite, UMR 8145, Lab MAP5, Paris, France

[3] Univ Exeter, Exeter, Devon, England

[4] Univ Paris Est, LAMA, UMR 8050, UPEM,CNRS,UPEC, Champs Sur Marne, France

来源：

STOCHASTICS AND DYNAMICS | 2020年 / 20卷 / 01期

基金：

英国工程与自然科学研究理事会; 欧洲研究理事会;

关键词：

Strong invariance principle; KMT approximation; nonuniformly expanding dynamical systems; Markov chain; STRONG APPROXIMATION; RANDOM-VARIABLES; PARTIAL SUMS; DECAY; KOMLOS;

D O I：

10.1142/S0219493720500021

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：

For a large class of quickly mixing dynamical systems, we prove that the error in the almost sure approximation with a Brownian motion is of order O ((log n)(a)) with a >= 2. Specifically, we consider nonuniformly expanding maps with exponential and stretched exponential decay of correlations, with one-dimensional Holder continuous observables.

引用

页数：28

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