Strong limit theorems for weighted sums of negatively associated random variables

被引：52

作者：

Jing, Bing-Yi ^{[2
]}

Liang, Han-Ying ^{[1
]}

机构：

[1] Tongji Univ, Dept Math, Shanghai 200092, Peoples R China

[2] Hong Kong Univ Sci & Technol, Dept Math, Kowloon, Hong Kong, Peoples R China

来源：

JOURNAL OF THEORETICAL PROBABILITY | 2008年 / 21卷 / 04期

基金：

中国国家自然科学基金;

关键词：

strong law; weighted sum; Cesaro mean; complete convergence; negatively associated random variable;

D O I：

10.1007/s10959-007-0128-4

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 establish strong laws for weighted sums of identically distributed negatively associated random variables. Marcinkiewicz-Zygmund's strong law of large numbers is extended to weighted sums of negatively associated random variables. Furthermore, we investigate various limit properties of Cesaro's and Riesz's sums of negatively associated random variables. Some of the results in the i.i.d. setting, such as those in Jajte (Ann. Probab. 31(1), 409-412, 2003), Bai and Cheng (Stat. Probab. Lett. 46, 105-112, 2000), Li et al. (J. Theor. Probab. 8, 49-76, 1995) and Gut (Probab. Theory Relat. Fields 97, 169-178, 1993) are also improved and extended to the negatively associated setting.

引用

页码：890 / 909

页数：20

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