Convergence of sequences of pairwise independent random variables

被引：4
|
作者：
Etemadi, N [1 ]
Lenzhen, A [1 ]
机构：
[1] Dept Math Stat & Comp Sci, Chicago, IL 60607 USA
来源：
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2004年 / 132卷 / 04期
关键词：
limit theorems; pairwise independence;
D O I：
10.1090/S0002-9939-03-07236-8
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In spite of the fact that the tail sigma-algebra of a sequence of pairwise independent random variables may not be trivial, we have discovered that if such a sequence converges in probability or almost everywhere, then the limit has to be a constant. This enables us to provide necessary and sufficient conditions for its convergence, in terms of its marginal distribution functions.
引用
收藏
页码：1201 / 1202
页数：2
相关论文
共 50 条
  • [1] ON THE CONVERGENCE OF SERIES OF PAIRWISE INDEPENDENT RANDOM-VARIABLES
    CSORGO, S
    TANDORI, K
    TOTIK, V
    ACTA MATHEMATICA HUNGARICA, 1985, 45 (3-4) : 445 - 450
  • [2] Almost everywhere convergence for sequences of pairwise NQD random variables
    Yang, Weiguo
    Zhu, Daying
    Gao, Rong
    COMMUNICATIONS IN STATISTICS-THEORY AND METHODS, 2017, 46 (05) : 2494 - 2505
  • [3] On convergence for sequences of pairwise negatively quadrant dependent random variables
    Yongfeng Wu
    Guangjun Shen
    Applications of Mathematics, 2014, 59 : 473 - 487
  • [4] On convergence for sequences of pairwise negatively quadrant dependent random variables
    Wu, Yongfeng
    Shen, Guangjun
    APPLICATIONS OF MATHEMATICS, 2014, 59 (04) : 473 - 487
  • [5] A note on the complete convergence for sequences of pairwise NQD random variables
    Huang, Haiwu
    Wang, Dingcheng
    Wu, Qunying
    Zhang, Qingxia
    JOURNAL OF INEQUALITIES AND APPLICATIONS, 2011,
  • [6] A note on the complete convergence for sequences of pairwise NQD random variables
    Haiwu Huang
    Dingcheng Wang
    Qunying Wu
    Qingxia Zhang
    Journal of Inequalities and Applications, 2011
  • [7] Convergence of weighted sums for sequences of pairwise NQD random variables
    Wu, Yongfeng
    Guo, Mingle
    COMMUNICATIONS IN STATISTICS-THEORY AND METHODS, 2016, 45 (20) : 5977 - 5989
  • [8] Complete convergence for weighted sums of pairwise independent random variables
    Ge, Li
    Liu, Sanyang
    Miao, Yu
    OPEN MATHEMATICS, 2017, 15 : 467 - 476
  • [9] On the Strong Law of Large Numbers for Sequences of Pairwise Independent Random Variables
    Korchevsky V.M.
    Journal of Mathematical Sciences, 2020, 244 (5) : 805 - 810
  • [10] On pairwise independent and independent exchangeable random variables
    Hu, TC
    STOCHASTIC ANALYSIS AND APPLICATIONS, 1997, 15 (01) : 51 - 57
12345