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2008 Generalized Gamma Convolutions, Dirichlet means, Thorin measures, with explicit examples
Lancelot F. James, Bernard Roynette, Marc Yor
Probab. Surveys 5: 346-415 (2008). DOI: 10.1214/07-PS118

Abstract

  • 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 processes.

  • To 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.

Citation

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Lancelot F. James. Bernard Roynette. Marc Yor. "Generalized Gamma Convolutions, Dirichlet means, Thorin measures, with explicit examples." Probab. Surveys 5 346 - 415, 2008. https://doi.org/10.1214/07-PS118

Information

Published: 2008
First available in Project Euclid: 10 October 2008

zbMATH: 1189.60035
MathSciNet: MR2476736
Digital Object Identifier: 10.1214/07-PS118

Subjects:
Primary: 60E07 , 60E10 , 60G51 , 60G52 , 60G57

Keywords: Dirichlet processes , Generalized Gamma Convolutions (GGC) , Laplace transform , Stieltjes transform , Wiener Gamma representation

Rights: Copyright © 2008 The Institute of Mathematical Statistics and the Bernoulli Society

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