Titre :

On the law of homogeneous stable functionals

Auteur(s) :

Letemplier, Julien [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Simon, Thomas [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]

Titre de la revue :

ESAIM: Probability and Statistics

Pagination :

82-111

Éditeur :

EDP Sciences

Date de publication :

2019-03-14

ISSN :

1292-8100

Mot(s)-clé(s) en anglais :

Beta random variable
exponential functional
homogeneous functional
infinite divisibility
stable Lévy process
time-change

Discipline(s) HAL :

Mathématiques [math]

Résumé en anglais : [en]

Let $A$ be the $L_q$ -functional of a stable Lévy process starting from one and killed when crossing zero. We observe that $A$ can be represented as the independent quotient of two infinite products of renormalized Beta ...
Lire la suite >Let $A$ be the $L_q$ -functional of a stable Lévy process starting from one and killed when crossing zero. We observe that $A$ can be represented as the independent quotient of two infinite products of renormalized Beta random variables. The proof relies on Markovian time change, the Lamperti transformation, and an explicit computation performed by Kuznetsov and Pardo on perpetuities of hypergeometric Lévy processes. This representation allows us to retrieve several factorizations previously shown by various authors, and also to derive new ones. We emphasize the connections between A and more standard positive random variables. We also investigate the law of Riemannian integrals of stable subordinators. Finally, we derive several distributional properties of A related to infinite divisibility, self-decomposability, and the generalized Gamma convolution.Lire moins >

Langue :

Anglais

Comité de lecture :

Oui

Audience :

Internationale

Vulgarisation :

Non

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL

Date de dépôt :

2025-01-24T14:31:29Z