Generalized Gamma convolutions, Dirichlet means, Thorin measures with explicit examples

Lancelot F. James (1) , Bernard Roynette (2, 3) , Marc Yor (4, 5)

1 HKUST - Hong Kong University of Science and Technology
2 IECN - Institut Élie Cartan de Nancy
3 TOSCA - Simuler et calibrer des modèles stochastiques
4 LPMA - Laboratoire de Probabilités et Modèles Aléatoires
5 IUF - Institut universitaire de France

In section 1, we present a number of classical results concerning the generalized Gamma convolution ( : GGC) variables, their Wiener-Gamma representations, and relation with Dirichlet processes. To a GGC variable, one may associate a unique Thorin measure. Let $G$ a positive r.v. and $\Gamma_t(G)$

Mots clés: Laplace transform; Generalized Gamma Convolutions (GGC); Wiener Gamma representation; Stieltjes transform; Dirichlet processes

Domaines: Probabilités [math.PR]

Lancelot F. James, Bernard Roynette, Marc Yor. Generalized Gamma convolutions, Dirichlet means, Thorin measures with explicit examples. Probability Surveys, 2008, 5, pp.346-415. ⟨10.1214/07-PS118⟩. ⟨hal-00174743⟩