Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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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)
  • Received : 2014.07.15
  • Published : 2015.03.01
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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.

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