THE SECOND CENTRAL LIMIT THEOREM FOR MARTINGALE DIFFERENCE ARRAYS

被引：1

作者：

Bae, Jongsig ^{[1
]}

Jun, Doobae ^{[2
]}

Levental, Shlomo ^{[3
]}

机构：

[1] Sungkyunkwan Univ, Inst Basic Sci, Dept Math, Suwon 440746, South Korea

[2] Gyeongsang Natl Univ, Dept Math & Ring, Jinju 660701, South Korea

[3] Michigan State Univ, Dept Stat & Probabil, E Lansing, MI 48824 USA

来源：

BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY | 2014年 / 51卷 / 02期

关键词：

central limit theorem; martingale difference array; bracketing entropy; majorizing measure; eventual uniform equicontinuity; UNIFORM CLT; ENTROPY;

D O I：

10.4134/BKMS.2014.51.2.317

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In Bae et al. [2], we have considered the uniform CLT for the martingale difference arrays under the uniformly integrable entropy. In this paper, we prove the same problem under the bracketing entropy condition. The proofs are based on Freedman inequality combined with a chaining argument that utilizes rnajorizing measures. The results of present paper generalize those for a sequence of stationary martingale differences. The results also generalize independent problems.

引用

页码：317 / 328

页数：12

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