$φ$-混合序列加权和的完全收敛性

数学物理学报 ›› 2018, Vol. 38 ›› Issue (6): 1095-1102.

$φ$-混合序列加权和的完全收敛性

章志华¹(),陈平炎^2,*()

¹ 广东财经大学经济学院广州 510320
² 暨南大学数学系广州 510632

收稿日期:2017-02-18 出版日期:2018-12-26 发布日期:2018-12-27
通讯作者: 陈平炎 E-mail:zzhjnu@163.com;tchenpy@jnu.edu.cn
作者简介:章志华, E-mail:zzhjnu@163.com
基金资助:
国家自然科学基金(11271161);教育部人文社科基金青年项目(17YJC910010)

Complete Convergence for Weighted Sums for $φ$-Mixing Random Variables

Zhihua Zhang¹(),Pingyan Chen^2,*()

¹ Faculty of Economics, Guangdong University of Finance and Economics, Guangzhou 510320
² Department of Mathematics, Jinan University, Guangzhou 510632

Received:2017-02-18 Online:2018-12-26 Published:2018-12-27
Contact: Pingyan Chen E-mail:zzhjnu@163.com;tchenpy@jnu.edu.cn
Supported by:
Supported by the NSFC(11271161);the HSSYFMOEC(17YJC910010)

摘要/Abstract

摘要：

该文把Chen和Sung（文献[1]）的一个关于同分布NA随机变量序列加权和最大值完全收敛性结果推广到了$φ$-混合随机变量序列情形.由于已有文献所用的工具本质上是部分和最大值指数型概率不等式，而对于$φ$-混合随机变量序列而言，没有那么好的指数型不等式，因此原有的证明方法已失效.该文将应用$φ$-混合随机变量序列部分和最大值的2-阶Marcinkiewicz-Zygmund矩不等式，结合再截尾方法，获得了理想的结果.该文的证明方法不同于已有结果的证明方法.

关键词: $φ$-混合序列')"> $φ$-混合序列, 加权和, 完全收敛性

Abstract:

The paper obtains the complete convergence for the maximun weighted sums, which improved and extended the result of Chen and Sung[1] from NA sequence to $φ$-mixing random variables. The main tool in Chen and Sung[1] is the exponent inequality of NA sequence, but no one knows wether the coresponding exponent inequality holds or not for $φ$-mixing random variables, so a different method is needed. In fact, we use only the maximun moment inequality and a new truncated method to prove the main result.

Key words: $φ$-Mixing sequence ')"> $φ$-Mixing sequence , Weighted sum, Complete convergence

中图分类号:

O211.4

章志华,陈平炎. $φ$-混合序列加权和的完全收敛性[J]. 数学物理学报, 2018, 38(6): 1095-1102.

Zhihua Zhang,Pingyan Chen. Complete Convergence for Weighted Sums for $φ$-Mixing Random Variables[J]. Acta mathematica scientia,Series A, 2018, 38(6): 1095-1102.

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