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http://dx.doi.org/10.4134/JKMS.2015.52.2.431

EXTENSIONS OF SEVERAL CLASSICAL RESULTS FOR INDEPENDENT AND IDENTICALLY DISTRIBUTED RANDOM VARIABLES TO CONDITIONAL CASES  

Yuan, De-Mei (School of Mathematics and Statistics Chongqing Technology and Business University)
Li, Shun-Jing (School of Mathematics and Statistics Chongqing Technology and Business University)
Publication Information
Journal of the Korean Mathematical Society / v.52, no.2, 2015 , pp. 431-445 More about this Journal
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;
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