On Uniform Nonintegrability and Weak Uniform Nonintegrability of a Sequence of Random Variables with Respect to a Nonnegative Array

Abstract

Chandra, Hu and Rosalsky^[1] introduced the notion of a sequence of random variables being uniformly nonintegrable and they established a de La Vallée Poussin type criterion for this notion. Inspired by the Chandra, Hu and Rosalsky^[1] article, Hu and Peng^[2] introduced the weaker notion of a sequence of random variables being weakly uniformly nonintegrable and they also established a de La Vallée Poussin type criterion for this notion using a modification of the Chandra, Hu and Rosalsky^[1] argument. In this correspondence, we introduce the more general notion of uniform nonintegrability and weak uniform nonintegrability with respect to an array of nonnegative real numbers together with a de La Vallée Poussin type criterion for this notion. This criterion immediately yields as particular cases the criteria of Chandra, Hu and Rosalsky^[1] and Hu and Peng^[2], and it has a substantially simpler and more straightforward proof.

Keywords

Sequence of uniformly nonintegrable random variables Sequence of weakly uniformly nonintegrable random variables de la Vallée Poussin criterion for uniform integrability de La Vallé Poussin type criterion for uniform nonintegrability and for weak uniform nonintegrability array of nonnegative real numbers

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References

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