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同分布 ρ 混合序列的最大值不等式及其应用

陈平炎   

  1. 暨南大学数学系 广州 510630
  • 收稿日期:2004-02-12 修回日期:2005-12-24 出版日期:2006-10-25 发布日期:2006-10-25
  • 通讯作者: 陈平炎
  • 基金资助:
    国家自然科学基金(60574002)资助

Maximal Inequalities for Identically Distributed ρ Mixing Random Variables and Applications

Chen Pingyan   

  1. Department of Mathematics, Jinan University, Guangzhou 510630
  • Received:2004-02-12 Revised:2005-12-24 Online:2006-10-25 Published:2006-10-25
  • Contact: Chen Pingyan

摘要: 设Xn,n≥1是同分布的ρ混合序列, 记Sn=∑ni=1 Xi. 该文讨论了max1in|Si|i (n1)的分布函数的上界. 作为应用,获得了随机变量supn1|Sn|n的1阶矩及p(>1)阶矩分别存在有限的充分
必要条件,这是一个与独立同分布场合相一致的结果.

关键词: ρ 混合序列, 最大值不等式;极大值函数的矩

Abstract:

Let {Xn,n1} be a sequence of identically distributed
˜ρ mixing random variables and Sn=ni=1Xi(n1). The paper discusses the upper bound of the distributions of max1in|Si|i(n1), and the sufficient and necessary conditions of the 1-th and p-th(p>1) moments of supn1|Sn|n are obtained, which are as same as the case of the independent identically distributions.

Key words: ρ mixing sequence, Maximal inequality, The moment of
supremum function.

中图分类号: 

  • 60F05