Cesaro α-Integrability and laws of large numbers I

被引：23

作者：

Chandra, TK ^{[1
]}

Goswami, A ^{[1
]}

机构：

[1] Indian Stat Inst, Div Theoret Stat & Math, Kolkata 700108, W Bengal, India

来源：

JOURNAL OF THEORETICAL PROBABILITY | 2003年 / 16卷 / 03期

关键词：

uniform integrability; pairwise independent; phi-mixing sequence;

D O I：

10.1023/A:1025620532404

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 [统计学]; 070103 [概率论与数理统计]; 0714 [统计学];

摘要：

For a sequence of integrable random variables, we introduce a new set of conditions called Cesaro alpha-Integrability and Strong Cesaro alpha-Integrability and show that, for alpha< 1/2, these conditions that are strictly weaker than Cesaro Uniform Integrability and Strong Cesaro Uniform Integrability respectively, are sufficient for WLLN and SLLN to hold for a sequence of pairwise independent random variables. For some special kinds of dependent sequences of random variables also, Cesaro alpha-integrability for appropriate alpha is shown to be sufficient for WLLN to hold.

引用

页码：655 / 669

页数：15