[1]高 萍.一类随机变量序列加权和的强大数定律[J].延边大学学报(自然科学版),2021,47(03):212-215.
　GAO Ping.The strong law of large numbers for weighted sums of some random variables[J].Journal of Yanbian University,2021,47(03):212-215.
点击复制

一类随机变量序列加权和的强大数定律

《延边大学学报(自然科学版)》[ISSN:1004-4353/CN:22-1191/N] 卷: 第47卷 期数: 2021年03期 页码: 212-215 栏目: 基础科学研究 出版日期: 2021-10-20
Title:
The strong law of large numbers for weighted sums of some random variables
文章编号:
1004-4353(2021)03-0212-04
作者:
高 萍
(厦门工学院数据科学与智能工程学院,福建厦门361021)
Author(s):
GAO Ping
( Data Science and Intelligent Engineering School, Xiamen Institute of Technology, Xiamen 361021, China )
关键词:
随机控制;  强大数定律;  Rosenthal型不等式;  加权和
Keywords:
stochastically dominated;  strong law of large numbers;  Rosental type inequality;  weighted sums
分类号:
O211
文献标志码:
A
摘要:
研究一类被随机控制的随机变量序列加权和的Marcinkiewicz -Zygmund型强大数定律.在满足Rosenthal型不等式的情况下得到了比经典Marchinkiewicz -Zygmund型强大数定律稍强的大数定律,并将所得结论推广到了更为广泛的一类随机变量序列上.
Abstract:
A class of stochastically dominated Marcinkiewicz -Zygmund type strong law of large numbers for weighted sums of random variable is studied. Under the condition of satisfying Rosenthal type inequality, a law of large numbers which is slightly stronger than the classical Marchinkiewicz -Zygmund type strong law of large numbers is obtained, and the obtained results is extended to a wider class of random variable sequences.

参考文献/References:

[1] BAI Z D, CHENG P E.Marcinkiewicz strong laws for linear statistics[J].Stat Probab Lett, 2000,46:105-112.
[2] WU Q.A strong limit theorem for weighted sums of sequences of negatively dependent random variables[J].J Inequal Appl, 2010,1:1-8.
[3] HUANG H, WANG D, PENG J.On the strong law of large numbers for weighted sums of φ - mixing random variables[J].J Math Inequal, 2014,8(3):465-473.
[4] WU Y, WANG X, HU S, et al.Weighted version of strong law of large numbers for a class of random variables and its applications[J].Test, 2018,27:379-406.
[5] YI Y, CHEN P, SUNG S H.Strong laws for weighted sums of random variables satisfying generalized Rosenthal type inequalities[J].J Inequal Appl, 2020,43:1-8.
[6] 吴群英.混合序列的概率极限理论[M].北京:科学出版社,2006.
[7] CUZICK J.A strong law for weighted sums of i.i.d.random variables[J].J Theor Probab, 1995,8:625-641.
[8] CHANDRA T K, GHOSAL S.Extensions of the strong law of large numbers of Marcinkiewicz and Zygmund for dependent variables[J].Acta Math Hung, 1996,71(4):327-336.

备注/Memo

收稿日期: 2021-04-21
基金项目: 福建省中青年教师教育科研项目(JT180771)
作者简介: 高萍(1983—),女,硕士,讲师,研究方向为概率极限理论.

更新日期/Last Update: 2021-10-20