阵列的单对数极限律

doi:10.6040/j.issn.1671-9352.0.2014.015

山东大学学报（理学版） ›› 2014, Vol. 49 ›› Issue (07): 75-79.doi: 10.6040/j.issn.1671-9352.0.2014.015

阵列的单对数极限律

冯志伟

暨南大学统计系, 广东广州 510630

收稿日期:2014-01-09 出版日期:2014-07-20 发布日期:2014-09-15
作者简介:冯志伟（1990- ），男，硕士研究生，研究方向为极限理论与分析概率. E-mail：fengzw1990@126.com
基金资助:
国家自然科学基金资助项目（11271161）

The limit law of the single logarithm for arrays

FENG Zhi-wei

Department of Statistics, Jinan University, Guangzhou 510630, Guangdong, China

Received:2014-01-09 Online:2014-07-20 Published:2014-09-15

摘要/Abstract

摘要： 利用随机变量阵列的强逼近，得到了随机变量阵列的单对数极限律，深化了已有的研究结果。同时，对取值于Banach空间的随机元阵列也得到了类似的结果。

关键词: 单对数律, 单对数极限律, 随机变量阵列, 随机元

Abstract: The limit law of the single logarithm by arrays of i.i.d random variables is obtained through the strong approximations, deepening the existing result. And the similar result is got in Banach space setting.

Key words: array of random variables, random element, the limit law of the single logarithm, the law of the single logarithm

中图分类号:

O211.4

冯志伟. 阵列的单对数极限律[J]. 山东大学学报（理学版）, 2014, 49(07): 75-79.

FENG Zhi-wei. The limit law of the single logarithm for arrays[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2014, 49(07): 75-79.

参考文献

[1] HARTMAN P, WINTNER P. On the law of the iterated logarithm[J]. Am J Math, 1941, 63:169-176.
[2] STRASSEN V. A converse to the law of the iterated logarithm[J]. Z Wahrscheinlichkeitstheor Verwandte Geb, 1966, 4:265-268.
[3] CHEN Xia. The limit law of the iterated logarithm [J/OL]. J Theoret Probab,2013[2013-12-10].http://dx.doi.org/10.1007/S 10959-013-0481-4.
[4] LI Deli, LIANG Hanying. The limit law of the iterated logarithm in Banach space[J]. Statistics and Probability Letters, 2013, 83:1800-1804.
[5] HU T C, WEBERN C. On the rate of convergence in the strong law of large number for arrays[J]. Bull Austral Math Soc, 1992, 45:279-282.
[6] LI Deli, RAO M B, TOMKINS R J. A strong law for B-valued arrays[J]. Proc Amer Math Soc, 1995, 123:3205-3212.
[7] QI Y C. On the strong convergence of arrays[J]. Bull Austral Math Soc, 1994, 50:219-223.
[8] 汪嘉冈.现代概率论基础[M].上海:复旦大学出版社, 2005: 98-99. WANG Jiagang. Modern probability theory[M]. Shanghai: Fudan University Press, 2005:98-99.
[9] LI Deli, HUANG Meiling, ROSALSKYA. Strong invariance principles for arrays[J]. Bull Inst Math Acad Sinica, 2000, 28:167-181.

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阵列的单对数极限律

The limit law of the single logarithm for arrays

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