Mathematics > Probability
[Submitted on 29 Aug 2007 (v1), last revised 22 Jan 2009 (this version, v2)]
Title:Generalized Gamma Convolutions, Dirichlet means, Thorin measures, with explicit examples
View PDFAbstract: In Section 1, we present a number of classical results concerning the Generalized Gamma Convolution (:GGC) variables, their Wiener-Gamma representations, and relation with the Dirichlet this http URL a GGC variable, one may associate a unique Thorin measure. Let $G$ a positive r.v. and $\Gamma_t(G)$ (resp. $\Gamma_t(1/G))$ the Generalized Gamma Convolution with Thorin measure $t$-times the law of $G$ (resp. the law of $1/G$). In Section 2, we compare the laws of $\Gamma_t(G)$ and $\Gamma_t(1/G)$.In Section 3, we present some old and some new examples of GGC variables, among which the lengths of excursions of Bessel processes straddling an independent exponential time.
Submission history
From: Lancelot F. James [view email][v1] Wed, 29 Aug 2007 10:44:08 UTC (45 KB)
[v2] Thu, 22 Jan 2009 11:11:21 UTC (211 KB)
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