Rates of convergence in the strong invariance principle under projective criteria

被引：8

作者：

Dedecker, Jerome ^{[1
]}

Doukhan, Paul ^{[2
]}

Merlevede, Florence ^{[3
]}

机构：

[1] Univ Paris 05, F-75270 Paris 06, France

[2] Univ Cergy Pontoise, Cergy Pontoise, France

[3] Univ Paris Est, Paris, France

来源：

ELECTRONIC JOURNAL OF PROBABILITY | 2012年 / 17卷

关键词：

almost sure invariance principle; strong approximations; weak dependence; Markov chains; CENTRAL-LIMIT-THEOREM; DEPENDENT RANDOM-VARIABLES; STATIONARY-PROCESSES; PARTIAL-SUMS; APPROXIMATION THEOREMS; MARKOV-CHAINS; ITERATED LOGARITHM; DYNAMICAL-SYSTEMS; MIXING SEQUENCES; INDEPENDENT RVS;

D O I：

10.1214/EJP.v17-1849

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 give rates of convergence in the strong invariance principle for stationary sequences satisfying some projective criteria. The conditions are expressed in terms of conditional expectations of partial sums of the initial sequence. Our results apply to a large variety of examples. We present some applications to a reversible Markov chain, to symmetric random walks on the circle, and to functions of dependent sequences.

引用

页码：1 / 31

页数：31

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