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.
Qianmin Chen and Jicheng Liu
Huazhong University of Science and Technology, Huazhong University of Science and Technology
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
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