A family of generalized gamma convoluted variables

Bernard Roynette (1) , Pierre P. Vallois (1) , Marc Yor (2)

1 IECN - Institut Élie Cartan de Nancy
2 LPMA - Laboratoire de Probabilités et Modèles Aléatoires

This paper consists of three parts: in the first part, we describe a family of generalized gamma convoluted (abbreviated as GGC) variables. In the second part, we use this description toprove that several r.v.'s, related to the length of excursions away from 0 for a recurrent linear diffusion on $\Bbb R_+$, are GGC. Finally, in the third part, we apply our results to the case of Bessel processes with dimension $d = 2(1 - \alpha)(0 < d < 2, or 0 < \alpha < 1).

Domaines: Probabilités [math.PR]; Statistiques [math.ST]; Théorie [stat.TH]

Bernard Roynette, Pierre P. Vallois, Marc Yor. A family of generalized gamma convoluted variables. Probability and Mathematical Statistics, 2009, 29 (2), pp.181-204. ⟨hal-00292334⟩