The paper contains a new and elementary proof of the fact that if α ∈ (0,1] then every scale mixture of a symmetric α-stable probability measure is infinitely divisible. This property is known to be a consequence of Kelker's result for the Cauchy distribution and some nontrivial properties of completely monotone functions. It is known that this property does not hold for α = 2. The problem discussed in the paper is still open for α ∈ (1,2).
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc90-0-5,
author = {Gra\.zyna Mazurkiewicz},
title = {On the infinite divisibility of scale mixtures of symmetric a-stable distributions, a [?] (0,1]},
journal = {Banach Center Publications},
volume = {89},
year = {2010},
pages = {79-82},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc90-0-5}
}
Grażyna Mazurkiewicz. On the infinite divisibility of scale mixtures of symmetric α-stable distributions, α ∈ (0,1]. Banach Center Publications, Tome 89 (2010) pp. 79-82. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc90-0-5/