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

De-Mei Yuan|Shun-Jing Li
대한수학회 (The Korean Mathematical Society)|2015.03|대한수학회지 (Journal of the KMS)|제52권 제2호|pp. 431-445

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참고문헌

키워드

conditional independenceconditional identical distributionconditional Kolmogorov convergence criterionconditional Marcinkiewicz-Zygmund inequalitiesconditional Marcinkiewicz-Zygmund strong law
주제분류수학

초록

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 Lp for conditionally independent and conditionally identically distributed random variables are established, respectively.

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 Lp for conditionally independent and conditionally identically distributed random variables are established, respectively.

참고문헌 (20)

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관련 논문AI추천

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