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On free stable distributions
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| Title: | On free stable distributions |
| Authors: | Hasebe, Takahiro Browse this author | | Kuznetsov, Alexey Browse this author |
| Keywords: | free stable distribution | | stable distribution | | Mellin transform |
| Issue Date: | 19-Aug-2014 |
| Publisher: | Institute of Mathematical Statistics |
| Journal Title: | Electronic Communications in Probability |
| Volume: | 19 |
| Issue: | 56 |
| Start Page: | 1 |
| End Page: | 12 |
| Publisher DOI: | 10.1214/ECP.v19-3443 |
| 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. |
| Rights: | http://creativecommons.org/licenses/by/3.0/ |
| Type: | article |
| URI: | http://hdl.handle.net/2115/57181 |
| Appears in Collections: | 理学院・理学研究院 (Graduate School of Science / Faculty of Science) > 雑誌発表論文等 (Peer-reviewed Journal Articles, etc)
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Submitter: 長谷部 高広
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