Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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THE CONDITIONAL BOREL-CANTELLI LEMMA AND APPLICATIONS

  • Chen, Qianmin (School of Mathematics and Statistics Huazhong University of Science and Technology) ;
  • Liu, Jicheng (School of Mathematics and Statistics Huazhong University of Science and Technology)
  • Received : 2016.01.17
  • Published : 2017.03.01
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Abstract

In this paper, we establish some conditional versions of the first part of the Borel-Cantelli lemma. As its applications, we study strong limit results of $\mathfrak{F}$-independent random variables sequences, the convergence of sums of $\mathfrak{F}$-independent random variables and the conditional version of strong limit results of the concomitants of order statistics.

Keywords

Acknowledgement

Supported by : NSFs of China, HUST

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