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.
De-Mei Yuan and Shun-Jing Li
Chongqing Technology and Business University, Chongqing Technology and Business University
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
2014; 51(1): 1-15
2017; 54(2): 441-460
2016; 53(6): 1275-1292
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