A note on random variables with an infinite absolute first moment

In this correspondence, we prove that if X is a random variable with P(X=0)=0 and E|X|=∞, then there exists a continuous function G on (0,∞) with 0<G(x)↑∞ and xG(x)↑∞ as 0<x↑∞ such that E(|X|/G(|X|))=∞. An application of this result pertaining to the Kolmogorov strong law of large numbers is established.

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Year of publication:	2015
Authors:	Hu, Tien-Chung ; Rosalsky, Andrew
Published in:	Statistics & Probability Letters. - Elsevier, ISSN 0167-7152. - Vol. 97.2015, C, p. 212-215
Publisher:	Elsevier
Subject:	Infinite absolute first moment \| Sums of independent and identically distributed random variables \| Kolmogorov strong law of large numbers \| Almost sure convergence

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Type of publication:	Article
Source:	RePEc - Research Papers in Economics

Persistent link: https://ebvufind01.dmz1.zbw.eu/10011189320