Journal of the
Korean Mathematical Society
JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

Article

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J. Korean Math. Soc. 2017; 54(2): 441-460

Online first article December 7, 2016      Printed March 1, 2017

https://doi.org/10.4134/JKMS.j160036

Copyright © The Korean Mathematical Society.

The conditional Borel-Cantelli lemma and applications

Qianmin Chen and Jicheng Liu

Huazhong University of Science and Technology, Huazhong University of Science and Technology

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 $\sF$-independent random variables sequences, the convergence of sums of $\sF$-independent random variables and the conditional version of strong limit results of the concomitants of order statistics.

Keywords: conditional independence, conditional Borel-Cantelli lemma, order statistics, concomitant

MSC numbers: 60F15