Title	One dimensional stable distributions are back!
Creator	Fourati, Sonia
Publisher	Banff International Research Station for Mathematical Innovation and Discovery
Date Issued	2016-11-08T11:30
Description	It has been known for some time that extremal $\alpha$ stable variables ($S_{\alpha}$) are Generalized Gamma Convolutions. Recently, L. Bondesson has shown that the family of GGC distributions is stable by multiplicative convolution. I will exhibit a first consequence of this result with a short proof of the fact that $\alpha$-stable densities are hyperbolically completely monotone (HCM in short). This result was first obtained by T. Simon and P. Bosch. I will give a general representation of all positive $\alpha$-densities. This result can be used for numerical reasons and gives a new point of view on the famous Zolotarev result on unimodality problem. Also we obtain the optimal $\beta$ such that $S_{\alpha}^{\beta}$ has an HCM density.
Extent	41 minutes
Subject	Mathematics; Probability theory and stochastic processes; Functional analysis; Probability / statistical mechanics
Type	Moving Image
File Format	video/mp4
Language	eng
Notes	Author affiliation: INSA Rouen
Series	BIRS Workshop Lecture Videos (Oaxaca de Juárez (Mexico))
Date Available	2017-06-18
Provider	Vancouver : University of British Columbia Library
Rights	Attribution-NonCommercial-NoDerivatives 4.0 International
DOI	10.14288/1.0348332
URI	http://hdl.handle.net/2429/62014
Affiliation	Non UBC
Peer Review Status	Unreviewed
Scholarly Level	Faculty
Rights URI	http://creativecommons.org/licenses/by-nc-nd/4.0/
Aggregated Source Repository	DSpace

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One dimensional stable distributions are back! Fourati, Sonia

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