Journal of the
Korean Mathematical Society
JKMS

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

Article

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J. Korean Math. Soc. 2015; 52(2): 431-445

Printed March 1, 2015

https://doi.org/10.4134/JKMS.2015.52.2.431

Copyright © The Korean Mathematical Society.

Extensions of several classical results for independent and identically distributed random variables to conditional cases

De-Mei Yuan and Shun-Jing Li

Chongqing Technology and Business University, Chongqing Technology and Business University

Abstract

Extensions of the Kolmogorov convergence criterion and the Marcinkiewicz-Zygmund inequalities from independent random variables to conditional independent ones are derived. As their applications, a conditional version of the Marcinkiewicz-Zygmund strong law of large numbers and a result on convergence in $L^p$ for conditionally independent and conditionally identically distributed random variables are established, respectively.

Keywords: conditional independence, conditional identical distribution, conditional Kolmogorov convergence criterion, conditional Marcinkiewicz-Zygmund inequalities, conditional Marcinkiewicz-Zygmund strong law

MSC numbers: 60F15, 60F25