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2014 On free stable distributions
Takahiro Hasebe, Alexey Kuznetsov
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Electron. Commun. Probab. 19: 1-12 (2014). DOI: 10.1214/ECP.v19-3443


We investigate analytical properties of free stable distributions and discover many connections with their classical counterparts. Our main result is an explicit formula for the Mellin transform, which leads to explicit series representations for the characteristic function and for the density of a free stable distribution. All of these formulas bear close resemblance to the corresponding expressions for classical stable distributions. As further applications of our results, we give an alternative proof of the duality law due to Biane and a new factorization of a classical stable random variable into an independent (in the classical sense) product of a free stable random variable and a power of a Gamma(2) random variable.


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Takahiro Hasebe. Alexey Kuznetsov. "On free stable distributions." Electron. Commun. Probab. 19 1 - 12, 2014.


Accepted: 19 August 2014; Published: 2014
First available in Project Euclid: 7 June 2016

zbMATH: 1317.46049
MathSciNet: MR3254735
Digital Object Identifier: 10.1214/ECP.v19-3443

Primary: 46L54
Secondary: 60E07

Keywords: Free stable distribution , Mellin transform , stable distribution


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