On the rate of convergence in the strong law of large numbers for martingales

被引：11

作者：

Miao, Yu ^{[1
]}

Yang, Guangyu ^{[2
]}

Stoica, George ^{[3
]}

机构：

[1] Henan Normal Univ, Coll Math & Informat Sci, Xinxiang 453007, Henan Province, Peoples R China

[2] Zhengzhou Univ, Sch Math & Stat, Zhengzhou 450001, Henan Province, Peoples R China

[3] Univ New Brunswick, Dept Math Sci, St John, NB E2L 4L5, Canada

来源：

STOCHASTICS-AN INTERNATIONAL JOURNAL OF PROBABILITY AND STOCHASTIC PROCESSES | 2015年 / 87卷 / 02期

关键词：

martingale difference sequences; rate of convergence; complete convergence; regular cover;

D O I：

10.1080/17442508.2014.938075

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The aim of this note is to establish the Baum-Katz type rate of convergence in the Marcinkiewicz-Zygmund strong law of large numbers for martingales, which improves the recent works of Stoica [Series of moderate deviation probabilities for martingales, J. Math. Anal. Appl. 336 (2005), pp. 759-763; Baum-Katz-Nagaev type results for martingales, J. Math. Anal. Appl. 336 (2007), pp. 1489-1492; A note on the rate of convergence in the strong law of large numbers for martingales, J. Math. Anal. Appl. 381 (2011), pp. 910-913]. Furthermore, we also study some relevant limit behaviours for the uniform mixing process. Under some uniform mixing conditions, the sufficient and necessary condition of the convergence of the martingale series is established.

引用

页码：185 / 198

页数：14

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