Kolmogorov Type Law of the Logarithm for Arrays

被引：5

作者：

Hoffmann-Jorgensen, Jorgen ^{[1
]}

Miao, Yu ^{[2
]}

Li, Xiao Chun ^{[2
]}

Xu, Shou Fang ^{[3
]}

机构：

[1] Aarhus Univ, Dept Math, Aarhus, Denmark

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

[3] Xinxiang Univ, Dept Math & Informat Sci, Xinxiang 453000, Henan Province, Peoples R China

来源：

JOURNAL OF THEORETICAL PROBABILITY | 2016年 / 29卷 / 01期

关键词：

Kolmogorov's law of the logarithm; Independent random variables; Bernstein's inequality; Kolmogorov's inequality; ITERATED LOGARITHM; RANDOM-VARIABLES; LARGE NUMBERS; CONVERGENCE;

D O I：

10.1007/s10959-014-0574-8

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 the analogue of Kolmogorov-type law of the logarithm for an array of independent random variables. The main methods are to develop the classic Bernstein's and Kolmogorov's inequality and replace the boundedness condition by conditions on the cumulant transform.

引用

页码：32 / 47

页数：16

共 15 条

[1]

EGOROV VA, 1969, TEOR VEROYA PRIMEN, V14, P722

[2] The general form of the so-called law of the iterated logarithm [J].