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

Banach Center Publications (2010)

- Volume: 90, Issue: 1, page 79-82
- ISSN: 0137-6934

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topGrażyna 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 -

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