φ-混合序列,加权和,完全收敛性," /> φ-混合序列,加权和,完全收敛性,"/> φ-Mixing sequence ,Weighted sum,Complete convergence,"/> <inline-formula><tex-math id="M1"><span class="MathJax_Preview" style="color: inherit;"><span class="MJXp-math" id="MJXp-Span-10"><span class="MJXp-mrow" id="MJXp-Span-11"><span class="MJXp-mo" id="MJXp-Span-12" style="margin-left: 0em; margin-right: 0em;">φ</span></span></span></span><script type="math/tex" id="MathJax-Element-4">φ</script></tex-math></inline-formula>-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.

• 论文 • 上一篇    下一篇

φ-混合序列加权和的完全收敛性

章志华1(),陈平炎2,*()   

  1. 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 Chen2,*()   

  1. 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:

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