Moderate deviations for stationary sequences of bounded random variables

被引：7

作者：

Dedecker, Jerome ^{[1
]}

Merlevede, Florence ^{[2
,3
]}

Peligrad, Magda ^{[4
]}

Utev, Sergey ^{[5
]}

机构：

[1] Univ Paris 06, LSTA, F-75013 Paris, France

[2] Univ Paris Est Marne la Vallee, LAMA, F-77454 Marne La Vallee 2, France

[3] CNRS, UMR 8050, F-77454 Marne La Vallee 2, France

[4] Univ Cincinnati, Dept Math Sci, Cincinnati, OH 45221 USA

[5] Univ Nottingham, Sch Math Sci, Nottingham NG7 2RD, England

来源：

ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES | 2009年 / 45卷 / 02期

关键词：

Moderate deviations; Martingale approximation; Stationary processes; CENTRAL-LIMIT-THEOREM; MARKOV-CHAINS; MARTINGALES; INEQUALITY;

D O I：

10.1214/08-AIHP169

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：

In this paper we derive the moderate deviation principle for stationary sequences of bounded random variables under martingale-type conditions. Applications to functions of phi-mixing sequences, contracting Markov chains, expanding maps of the interval, and symmetric random walks on the circle are given.

引用

页码：453 / 476

页数：24

共 50 条

[21] MODERATE DEVIATIONS OF DEPENDENT RANDOM-VARIABLES RELATED TO CLT
WU, LM
ANNALS OF PROBABILITY, 1995, 23 (01): : 420 - 445
[22] Sharp large deviations for sums of bounded from above random variables
Fan, XieQuan
SCIENCE CHINA-MATHEMATICS, 2017, 60 (12) : 2465 - 2480
[23] Sharp large deviations for sums of bounded from above random variables
XieQuan Fan
Science China Mathematics, 2017, 60 : 2465 - 2480
[24] Sharp large deviations for sums of bounded from above random variables
FAN XieQuan
Science China Mathematics, 2017, 60 (12) : 2465 - 2480
[25] Moderate deviations and functional limits for random processes with stationary and independent increments
GAO Fuqing School of Mathematics and Statistics
Science China Mathematics, 2006, (12) : 1753 - 1767
[26] Moderate deviations and functional limits for random processes with stationary and independent increments
Fuqing Gao
Science in China Series A: Mathematics, 2006, 49 : 1753 - 1767
[27] Moderate deviations and functional limits for random processes with stationary and independent increments
Gao Fuqing
SCIENCE IN CHINA SERIES A-MATHEMATICS, 2006, 49 (12): : 1753 - 1767
[28] Moderate deviations for stationary processes
Wu, Wei Biao
Zhao, Zhibiao
STATISTICA SINICA, 2008, 18 (02) : 769 - 782
[29] MODERATE DEVIATIONS PRINCIPLE FOR INDEPENDENT RANDOM VARIABLES UNDER SUBLINEAR EXPECTATIONS
Zhou, Q. Q.
Logachov, A., V
SIBERIAN ELECTRONIC MATHEMATICAL REPORTS-SIBIRSKIE ELEKTRONNYE MATEMATICHESKIE IZVESTIYA, 2021, 18 : 817 - 826
[30] Local Precise Large and Moderate Deviations for Sums of Independent Random Variables
Cheng, Fengyang
Li, Minghua
CHINESE ANNALS OF MATHEMATICS SERIES B, 2016, 37 (05) : 753 - 766

← 1 2 3 4 5 →