数学季刊 ›› 2009, Vol. 24 ›› Issue (4): 551-560.

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关于α混合事件序列的第二Borel-Cantelli引理

  

  1. College of Science, Chongqing Technology and Business University

  • 收稿日期:2005-04-20 出版日期:2009-12-30 发布日期:2023-06-19
  • 作者简介:YUAN De-mei(1966-), male, native of Nanchong, Sichuan, an associate professor of Chongqing Technology and Business University, M.S.D., engages in probability limit theory.
  • 基金资助:
     Supported by the SCR of Chongqing Municipal Education Commission(KJ090703);

On the Second Borel-Cantelli Lemma for a-mixing Sequences of Events 

  1. College of Science, Chongqing Technology and Business University
  • Received:2005-04-20 Online:2009-12-30 Published:2023-06-19
  • About author:YUAN De-mei(1966-), male, native of Nanchong, Sichuan, an associate professor of Chongqing Technology and Business University, M.S.D., engages in probability limit theory.
  • Supported by:
     Supported by the SCR of Chongqing Municipal Education Commission(KJ090703);

摘要: In this paper, we give some conditions on diverging rate of series of the probabilities and converging rate of series of theα-mixing coefficients for sequences of events, under which the conclusion of the Second Borel-Cantelli Lemma holds. As corollaries, some moment conditions are obtained, under which the strong law of large numbers holds for sequences of identically distributed random variables.

关键词:  Borel-Cantelli lemma, strong mixing, a-mixing, strong law of large numbers

Abstract: In this paper, we give some conditions on diverging rate of series of the probabilities and converging rate of series of theα-mixing coefficients for sequences of events, under which the conclusion of the Second Borel-Cantelli Lemma holds. As corollaries, some moment conditions are obtained, under which the strong law of large numbers holds for sequences of identically distributed random variables.

Key words:  Borel-Cantelli lemma, strong mixing, a-mixing, strong law of large numbers

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