On the infinite divisibility of scale mixtures of symmetric α-stable distributions, α ∈ (0,1]

Grażyna Mazurkiewicz. "On the infinite divisibility of scale mixtures of symmetric α-stable distributions, α ∈ (0,1]." Banach Center Publications 90.1 (2010): 79-82. <http://eudml.org/doc/281601>.

@article{GrażynaMazurkiewicz2010,
abstract = {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).},
author = {Grażyna Mazurkiewicz},
journal = {Banach Center Publications},
keywords = {stable distribution; scale mixture; variance mixture},
language = {eng},
number = {1},
pages = {79-82},
title = {On the infinite divisibility of scale mixtures of symmetric α-stable distributions, α ∈ (0,1]},
url = {http://eudml.org/doc/281601},
volume = {90},
year = {2010},
}

TY - JOUR
AU - Grażyna Mazurkiewicz
TI - On the infinite divisibility of scale mixtures of symmetric α-stable distributions, α ∈ (0,1]
JO - Banach Center Publications
PY - 2010
VL - 90
IS - 1
SP - 79
EP - 82
AB - 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).
LA - eng
KW - stable distribution; scale mixture; variance mixture
UR - http://eudml.org/doc/281601
ER -