Lobachevskii Journal of Mathematics

, Volume 39, Issue 3, pp 331–339 | Cite as

Relative Weak Compactness of Sums of Random Variables

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Abstract

In this article sufficient conditions for relative weak compactness of sums centered by constants of pair-wise negatively associated randomvariables and for sums of squares of any random variables centered by their medians are given. These conditions become necessary and sufficient if random variables are independent. The conditions are inspired by classical conditions for weak convergence of sums of uniformly small random variables.

Keywords

Pair-wise negatively associated random variables relative weak compactness 

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Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.Faculty of Physics and MathematicsMoscow Region State UniversityMoscowRussia
  2. 2.Department of Statistics, Faculty of Computational Mathematics and CyberneticsMoscow State UniversityMoscowRussia

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