On a particular class of self-decomposable random variables : the durations of Bessel excursions straddling independent exponential times.

J. Bertoin (1) , T. Fujita (2) , Bernard Roynette (3, 4) , Marc Yor (1)

1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires
2 Graduate school of Commerce and Management [Tokyo]
3 IECN - Institut Élie Cartan de Nancy
4 OMEGA - Probabilistic numerical methods

The distributional properties of the duration of a recurrent Bessel process straddling an independent exponential time are studied in detail. Althrough our study may be considered as a particular case of M. Winkel's in [Wink], the infinite divisibility structure of these Bessel durations is particularly rich and we develop algebraic properties for a family of random variables arising from the Lévy measures of these durations.

Mots clés: Bessel processes; self-decomposability; beta-gamme algebra; general gamme convolutions

Domaines: Probabilités [math.PR]

J. Bertoin, T. Fujita, Bernard Roynette, Marc Yor. On a particular class of self-decomposable random variables : the durations of Bessel excursions straddling independent exponential times.. 2006. ⟨hal-00104879⟩