A Note on Uniform Nonintegrability of Random Variables
Probability
2016-06-08 v2
Abstract
In a recent paper \cite{CHR16}, Chandra, Hu and Rosalsky introduced the notion of a sequence of random variables being uniformly nonintegrable, and presented a list of interesting results on this uniform nonintegrability. In this note, we introduce a weaker definition on uniform nonintegrability (W-UNI for short) of random variables, present a necessary and sufficient condition for W-UNI, and give two equivalent characterizations of W-UNI, one of which is a W-UNI analogue of the celebrated de La Vall\'{e}e Poussin criterion for uniform integrability. In addition, we give some remarks, one of which gives a negative answer to the open problem raised in \cite{CHR16}.
Cite
@article{arxiv.1605.05434,
title = {A Note on Uniform Nonintegrability of Random Variables},
author = {Ze-Chun Hu and Xue Peng},
journal= {arXiv preprint arXiv:1605.05434},
year = {2016}
}
Comments
12 pages