A note on the almost sure central limit theorem for some dependent random variables

被引：15

作者：

Dudzinski, M ^{[1
]}

机构：

[1] Warsaw Univ Technol, Dept Math & Informat Sci, PL-00661 Warsaw, Poland

来源：

STATISTICS & PROBABILITY LETTERS | 2003年 / 61卷 / 01期

关键词：

central limit theorem; almost sure central limit theorem; weakly dependent random variables; Markov chains;

D O I：

10.1016/S0167-7152(02)00291-2

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 the almost sure central limit theorem for random variables fulfilling a general condition of dependence due to Doukhan and Louhichi (Stochastic Process. Appl. 84 (1999) 313). Our main tool for the proofs is a result from Peligrad and Shao (Statist. Probab. Lett. 22 (1995) 131). (C) 2003 Elsevier Science B.V. All rights reserved.

引用

页码：31 / 40

页数：10

共 8 条

[1] SOME LIMIT-THEOREMS IN LOG DENSITY [J].

BERKES, I ;

DEHLING, H .

ANNALS OF PROBABILITY, 1993, 21 (03) :1640-1670

[2] AN ALMOST EVERYWHERE CENTRAL LIMIT-THEOREM [J].

BROSAMLER, GA .

MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 1988, 104 :561-574

[3] A new weak dependence condition and applications to moment inequalities [J].

Doukhan, P ;

Louhichi, S .

STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 1999, 84 (02) :313-342

[4]

FICHTENHOLZ GM, 1966, RACHUNEK ROZNICZKOWY, V2

[5] A NOTE ON THE ALMOST SURE CENTRAL-LIMIT-THEOREM [J].

LACEY, MT ;

PHILIPP, W .

STATISTICS & PROBABILITY LETTERS, 1990, 9 (03) :201-205

[6]

Matula P., 1998, PROBAB MATH STAT-POL, V18, P411

[7] A NOTE ON THE ALMOST SURE CENTRAL-LIMIT-THEOREM FOR WEAKLY DEPENDENT RANDOM-VARIABLES [J].

PELIGRAD, M ;

SHAO, QM .

STATISTICS & PROBABILITY LETTERS, 1995, 22 (02) :131-136

[8] ON STRONG VERSIONS OF THE CENTRAL LIMIT-THEOREM [J].

SCHATTE, P .

MATHEMATISCHE NACHRICHTEN, 1988, 137 :249-256

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