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On free stable distributions


 
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1. Title Title of document On free stable distributions
 
2. Creator Author's name, affiliation, country Takahiro Hasebe; Hokkaido University; Japan
 
2. Creator Author's name, affiliation, country Alexey Kuznetsov; York University; Canada
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) free stable distribution, stable distribution, Mellin transform
 
3. Subject Subject classification 46L54, 60E07
 
4. Description Abstract 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.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) Marie Curie Actions – International Incoming Fellowships; Natural Sciences and Engineering Research Council of Canada.
 
7. Date (YYYY-MM-DD) 2014-08-19
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ecp.ejpecp.org/article/view/3443
 
10. Identifier Digital Object Identifier 10.1214/ECP.v19-3443
 
11. Source Journal/conference title; vol., no. (year) Electronic Communications in Probability; Vol 19
 
12. Language English=en en
 
14. Coverage Geo-spatial location, chronological period, research sample (gender, age, etc.)
 
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