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山东大学学报(理学版) ›› 2017, Vol. 52 ›› Issue (4): 13-20.doi: 10.6040/j.issn.1671-9352.0.2016.249

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ρ-混合序列的重对数律矩收敛的精确渐近性

张亚运,吴群英*   

  1. 桂林理工大学理学院, 广西 桂林 541006
  • 收稿日期:2016-06-03 出版日期:2017-04-20 发布日期:2017-04-11
  • 通讯作者: 吴群英(1961— ),女,博士,教授,研究方向为概率极限理论.E-mail:wqy666@glut.edu.cn E-mail:1477852085@qq.com
  • 作者简介:张亚运(1990— ),男,硕士研究生,研究方向为概率极限理论.E-mail:1477852085@qq.com
  • 基金资助:
    国家自然科学基金资助项目(11361019);广西自然科学基金资助项目(2015GXNSFAA139008)

Precise asymptotics in the law of iterated logarithm for the moment convergence of ρ-mixing sequences

ZHANG Ya-yun, WU Qun-ying*   

  1. College of Science, Guilin University of Technology, Guilin 541006, Guangxi, China
  • Received:2016-06-03 Online:2017-04-20 Published:2017-04-11

摘要: 假设{Xn,n≥1}为一列严平稳ρ-混合随机变量,期望为零,方差有限。设Sn=∑Xi, Mn=max1≤i≤n|Si|。利用ρ-混合随机变量的矩不等式和中心极限定理,得到了一类ρ-混合随机变量序列部分和以及部分和的最大值重对数矩收敛的精确渐近性。

关键词: 精确渐近性, 矩收敛, 重对数律, ρ-混合序列

Abstract: Let {Xn, n≥1}be a sequence of strictly stationary of ρ-mixing random variables with zero means and finite variances. Set Sn=∑Xi, Mn=max1≤i≤n|Si|. Using the moment inequality and the central limit theorem of the ρ-mixing random variables.The precise asymptotics in the law of iterated logarithm for the moment convergence of ρ-mixing random variables of the partial sum and the maximum of the partial sum are obtained.

Key words: moment convergence, ρ-mixing random variables, precise asymptotics, the law of iterated logarithm

中图分类号: 

  • O211
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