数学季刊 >

2016 , Vol. 31 >Issue 2: 162 - 170

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2016.02.007

NSD随机变量阵列的L_r收敛性

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  • School of Mathematical Sciences,Anhui University
ZHU Hua-yan(1994-), male, native of Hefei, Anhui, engages in probability limit theorem; SHEN Ai-ting(1979-), female, native of Hefei, Anhui, an associate professor of Anhui Universiry, Ph.D., engages in probability limit theorem; ZHANG Ying(1993-), female, native of Putian, Fujian, engages in probability limit theorem.

收稿日期: 2014-04-18

  网络出版日期: 2020-11-06

基金资助

Supported by the Provincial Natural Science Research Project of Anhui Colleges(KJ2015A018)； Supported by the Students Science Research Training Program of Anhui University(kyxl2013003)； Supported by the Students Innovative Training Project of Anhui University(201410357118)； Supported by the Quality Engineering Project of Anhui Province(2015jyxm045)； Supported by the Quality Improvement Project for Undergraduate Education of Anhui University(ZLTS2015035)；

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Lr Convergence for Arrays of Rowwise Negatively Superadditive Dependent Random Variables

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  • School of Mathematical Sciences,Anhui University
ZHU Hua-yan(1994-), male, native of Hefei, Anhui, engages in probability limit theorem; SHEN Ai-ting(1979-), female, native of Hefei, Anhui, an associate professor of Anhui Universiry, Ph.D., engages in probability limit theorem; ZHANG Ying(1993-), female, native of Putian, Fujian, engages in probability limit theorem.

Received date: 2014-04-18

  Online published: 2020-11-06

Supported by

Supported by the Provincial Natural Science Research Project of Anhui Colleges(KJ2015A018)； Supported by the Students Science Research Training Program of Anhui University(kyxl2013003)； Supported by the Students Innovative Training Project of Anhui University(201410357118)； Supported by the Quality Engineering Project of Anhui Province(2015jyxm045)； Supported by the Quality Improvement Project for Undergraduate Education of Anhui University(ZLTS2015035)；

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摘要

Let {Xnk, k ≥ 1, n ≥ 1} be an array of rowwise negatively superadditive dependent random variables and {an, n ≥ 1} be a sequence of positive real numbers such that an↑∞. Under some suitable conditions,Lr convergence of 1/an max 1≤j≤n |j∑k=1 Xnk| is studied. The results obtained in this paper generalize and improve some corresponding ones for negatively associated random variables and independent random variables. 

关键词： Lr convergence; convergence in probability; negatively superadditive dependent random variables

本文引用格式

朱华炎, 沈爱婷, 张颖 . NSD随机变量阵列的L_r收敛性[J]. 数学季刊, 2016 , 31(2) : 162 -170 . DOI: 10.13371/j.cnki.chin.q.j.m.2016.02.007

Abstract

Let {Xnk, k ≥ 1, n ≥ 1} be an array of rowwise negatively superadditive dependent random variables and {an, n ≥ 1} be a sequence of positive real numbers such that an↑∞. Under some suitable conditions,Lr convergence of 1/an max 1≤j≤n |j∑k=1 Xnk| is studied. The results obtained in this paper generalize and improve some corresponding ones for negatively associated random variables and independent random variables. 

Key words： Lr convergence; convergence in probability; negatively superadditive dependent random variables

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