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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2017, Vol. 34 ›› Issue (1): 38-46.doi: 10.3969/j.issn.1005-3085.2017.01.005

• • 上一篇    下一篇

两两NQD列的极限定理

宋明珠,   吴永锋   

  1. 铜陵学院数学与计算机学院，安徽  铜陵  244000
  • 收稿日期:2014-09-15 接受日期:2016-03-02 出版日期:2017-02-15 发布日期:2017-04-15
  • 基金资助:
    安徽省高校自然科学研究重点项目(KJ2014A255; KJ2016A705)；安徽省高校优秀青年人才支持计划重点项目(gxyqZD2016317).

Some Limit Theorems for Pairwise NQD Random Sequences

SONG Ming-zhu,   WU Yong-feng   

  1. School of Mathematics and Computer Science, Tongling University, Tongling, Anhui 244000
  • Received:2014-09-15 Accepted:2016-03-02 Online:2017-02-15 Published:2017-04-15
  • Supported by:
    The Key University Science Research Project of Anhui Province (KJ2014A255; KJ2016A705); the Key Project of Anhui Province University Outstanding Youth Talent Support Program (gxyqZD2016317).

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摘要：

本文主要研究了两两NQD列的完全收敛性和强大数定律．文中给出了两两NQD列的定义和推广的Kolmogorov型不等式，并利用推广的Kolmogorov型不等式，得到了两两NQD列的完全收敛性定理．本文构造了两个不增函数，利用不增函数的性质，得到了两两NQD列的强大数定律．本文得到的强大数定律与独立随机变量情况下的强大数定律相类似，进而推广了前人的研究成果．

关键词: 两两NQD列, 完全收敛性, 强大数定律, 极限定理

Abstract:

In this paper, we study the complete convergence properties and strong laws of large numbers for pairwise NQD random sequences. We present the definition of pairwise NQD random sequences and the Kolmogorov inequality to the case of pairwise NQD random sequences. Based on the Kolmogorov inequality, we obtain complete convergence properties of pairwise NQD random sequences. We construct two non-increasing functions based on the properties of non-increasing function, and obtain some strong laws of large number for pairwise NQD random sequences, which is similar to independent random variable sequences. The theorem obtained in this paper thus inclines to extend the related results presented in previous literatures.

Key words: pairwise NQD random sequences, complete convergence properties, strong laws of large numbers, limit theorems

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