m-NA随机变量部分和的若干强收敛性

doi:10.13371/j.cnki.chin.q.j.m.2018.02.008

数学季刊 ›› 2018, Vol. 33 ›› Issue (2): 172-180.doi: 10.13371/j.cnki.chin.q.j.m.2018.02.008

m-NA随机变量部分和的若干强收敛性

School of Mathematical Sciences, Anhui University

接受日期:2017-10-23 出版日期:2018-06-30 发布日期:2020-10-09
作者简介:PEI Wen-chen(1995-), male, native of Tongling, Anhui, B.S.D., engages in statistics; Corresponding author, WANG Xue-jun(1981-), male, native of Hefei, Anhui, a professor of Anhui Universiry, Ph.D., engages in probability theory and mathematical statistics.
基金资助:
Supported by the Natural Science Foundation of Anhui Province(1508085J06)； the Key Projects for Academic Talent of Anhui Province(gxbj ZD2016005)； the Students Innovative Training Project of Anhui University(201610357001)；

The Strong Convergence Properties for Partial Sums of m-NA Random Variables

School of Mathematical Sciences, Anhui University

Accepted:2017-10-23 Online:2018-06-30 Published:2020-10-09
About author:PEI Wen-chen(1995-), male, native of Tongling, Anhui, B.S.D., engages in statistics; Corresponding author, WANG Xue-jun(1981-), male, native of Hefei, Anhui, a professor of Anhui Universiry, Ph.D., engages in probability theory and mathematical statistics.
Supported by:
Supported by the Natural Science Foundation of Anhui Province(1508085J06)； the Key Projects for Academic Talent of Anhui Province(gxbj ZD2016005)； the Students Innovative Training Project of Anhui University(201610357001)；

摘要/Abstract

摘要： In this paper, by the three series theorem of m-negatively associated(m-NA,in short) random variables and the truncation method of random variables, we mainly investigated the strong convergence properties for partial sums of m-NA random variables.In addition, the Khintchine-Kolmogorov convergence theorem and Kolmogorov-type strong law of large numbers for m-NA random variables are also obtained. The results obtained in the paper generalize some corresponding ones for independent random variables and some dependent random variables.

关键词: m-NA random variables, Three series theorem, Strong convergence, Kolmogorov-type strong law of large numbers

Abstract: In this paper, by the three series theorem of m-negatively associated(m-NA,in short) random variables and the truncation method of random variables, we mainly investigated the strong convergence properties for partial sums of m-NA random variables.In addition, the Khintchine-Kolmogorov convergence theorem and Kolmogorov-type strong law of large numbers for m-NA random variables are also obtained. The results obtained in the paper generalize some corresponding ones for independent random variables and some dependent random variables.

Key words: m-NA random variables, Three series theorem, Strong convergence, Kolmogorov-type strong law of large numbers

中图分类号:

O211

汪勐航, 裴文宸, 张宇恒, 应晗璐, 王学军. m-NA随机变量部分和的若干强收敛性[J]. 数学季刊, 2018, 33(2): 172-180.

WANG Meng-hang, PEI Wen-chen, ZHANG Yu-heng, YING Han-lu, WANG Xue-jun. The Strong Convergence Properties for Partial Sums of m-NA Random Variables[J]. Chinese Quarterly Journal of Mathematics, 2018, 33(2): 172-180.

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[2]	毛伟, 韩修静, 陈波. 带跳的随机比例微分方程的半隐式Euler数值解法[J]. 数学季刊, 2011, 26(3): 405-409.
[3]	张和平, 叶留青. 不等式约束最优化问题的可行SQP下降算法及其收敛性[J]. 数学季刊, 2009, 24(3): 469-474.
[4]	梁庆文, 缪柏其, 王大鹏. 一类随机矩阵经验分布的强收敛性[J]. 数学季刊, 2006, 21(1): 28-32.
[5]	凌能祥, 杜雪樵. 相依样本下非参数回归函数基于分割估计的强相合性[J]. 数学季刊, 2005, 20(1): 28-33.
[6]	薛留根, 李雪臣, 马全甫. 平稳序列条件密度双重核估计的强收敛速度[J]. 数学季刊, 1999, 14(2): 1-10.

m-NA随机变量部分和的若干强收敛性

The Strong Convergence Properties for Partial Sums of m-NA Random Variables

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