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 <TEX>$L^p$</TEX> for conditionally independent and conditionally identically distributed random variables are established, respectively.
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