On the Mellin transforms of the perpetuity and the remainder variables associated to a subordinator

F. Hirsch , Marc Yor (1)

1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires

Results about the laws of the perpetuity and remainder variables associated to a subordinator are presented, with particular emphasis on their Mellin transforms, and multiplicative infinite divisibility property. Previous results by Bertoin-Yor (Electron. Commun. Probab. 6 (2001) 95-106) are incorporated in our discussion; important examples when the subordinator is the inverse local time of a diffusion are exhibited. Results of Urbanik (Probab. Math. Statist. 15 (1995) 493-513) are also discussed in detail; they appear to be too little known, despite the fact that quite a few of them have priority upon other works in this area.

Domaines: Probabilités [math.PR]

F. Hirsch, Marc Yor. On the Mellin transforms of the perpetuity and the remainder variables associated to a subordinator. Bernoulli, 2013, 19 (4), pp.1350-1377. ⟨10.3150/12-BEJSP01⟩. ⟨hal-00873674⟩