数学物理学报(英文版) ›› 2014, Vol. 34 ›› Issue (2): 301-312.doi: 10.1016/S0252-9602(14)60006-0

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ASYMPTOTIC PROPERTIES OF THE MOMENT CONVERGENCE FOR NA SEQUENCES

赵月旭   

  1. Department of Mathematics, Hangzhou Dianzi University, Hangzhou 310018, China
  • 收稿日期:2011-12-02 修回日期:2013-08-21 出版日期:2014-03-20 发布日期:2014-03-20
  • 基金资助:

    This work is supported by National Natural Science Foundation of China (11171303, 61273093) and the Specialized Research Fund for the Doctor Program of Higher Education (20090101110020).

ASYMPTOTIC PROPERTIES OF THE MOMENT CONVERGENCE FOR NA SEQUENCES

 ZHAO Yue-Xu   

  1. Department of Mathematics, Hangzhou Dianzi University, Hangzhou 310018, China
  • Received:2011-12-02 Revised:2013-08-21 Online:2014-03-20 Published:2014-03-20
  • Supported by:

    This work is supported by National Natural Science Foundation of China (11171303, 61273093) and the Specialized Research Fund for the Doctor Program of Higher Education (20090101110020).

摘要:

It is well-known that the complete convergence theorem for i.i.d. random vari-ables has been an active topic since the famous work done by Hsu and Robbins [6]. Chow [4]obtained a moment version of Hsu and Robbins series. However, the series tends to infinity whenever ε  goes to zero, so it is of interest to investigate the asymptotic behavior of the series
as ε goes to zero. This note gives some limit theorems of the series generated by moments for NA random variables.

关键词: Asymptotic property, rate of convergence, complete moment convergence, NA sequence

Abstract:

It is well-known that the complete convergence theorem for i.i.d. random vari-ables has been an active topic since the famous work done by Hsu and Robbins [6]. Chow [4]obtained a moment version of Hsu and Robbins series. However, the series tends to infinity whenever ε  goes to zero, so it is of interest to investigate the asymptotic behavior of the series
as ε goes to zero. This note gives some limit theorems of the series generated by moments for NA random variables.

Key words: Asymptotic property, rate of convergence, complete moment convergence, NA sequence

中图分类号: 

  • 60F15