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
收藏
页码：32 / 47
页数：16
相关论文
共 50 条
  • [31] ON THE LAW OF THE ITERATED LOGARITHM
    WEISS, M
    JOURNAL OF MATHEMATICS AND MECHANICS, 1959, 8 (01): : 121 - 132
  • [32] LAW OF ITERATED LOGARITHM
    TOMKINS, RJ
    ANNALS OF PROBABILITY, 1978, 6 (01): : 162 - 168
  • [33] Exponential tail estimates in the law of ordinary logarithm (LOL) for triangular arrays of random variables
    Formica, Maria Rosaria
    Vasil'ovich Kozachenko, Yuriy
    Ostrovsky, Eugeny
    Sirota, Leonid
    LITHUANIAN MATHEMATICAL JOURNAL, 2020, 60 (03) : 330 - 358
  • [34] ON REPEATED LOGARITHM LAW
    SARYMSAK.TA
    KUCHKARO.YK
    DOKLADY AKADEMII NAUK SSSR, 1968, 182 (02): : 272 - &
  • [35] Exponential tail estimates in the law of ordinary logarithm (LOL) for triangular arrays of random variables
    Maria Rosaria Formica
    Yuriy Vasil’ovich Kozachenko
    Eugeny Ostrovsky
    Leonid Sirota
    Lithuanian Mathematical Journal, 2020, 60 : 330 - 358
  • [36] ON LAW OF ITERATED LOGARITHM
    SLIVKA, J
    PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA, 1969, 63 (02) : 289 - &
  • [37] LAW OF ITERATED LOGARITHM
    TEICHER, H
    ANNALS OF PROBABILITY, 1974, 2 (04): : 714 - 728
  • [38] On the law of the iterated logarithm
    Erdos, P
    ANNALS OF MATHEMATICS, 1942, 43 : 419 - 436
  • [39] On the law of the iterated logarithm
    Hartman, P
    Wintner, A
    AMERICAN JOURNAL OF MATHEMATICS, 1941, 63 : 169 - 176
  • [40] A law of the single logarithm for weighted sums of arrays applied to bootstrap model selection in regression
    de Micheaux, Pierre Lafaye
    Leger, Christian
    STATISTICS & PROBABILITY LETTERS, 2012, 82 (05) : 965 - 971
12345