On the law of homogeneous stable functionals
Document type :
Article dans une revue scientifique: Article original
DOI :
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Title :
On the law of homogeneous stable functionals
Author(s) :
Letemplier, Julien [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Simon, Thomas [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Simon, Thomas [Auteur]

Laboratoire Paul Painlevé - UMR 8524 [LPP]
Journal title :
ESAIM: Probability and Statistics
Pages :
82-111
Publisher :
EDP Sciences
Publication date :
2019-03-14
ISSN :
1292-8100
English keyword(s) :
Beta random variable
exponential functional
homogeneous functional
infinite divisibility
stable Lévy process
time-change
exponential functional
homogeneous functional
infinite divisibility
stable Lévy process
time-change
HAL domain(s) :
Mathématiques [math]
English abstract : [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 ...
Show more >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.Show less >
Show more >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.Show less >
Language :
Anglais
Peer reviewed article :
Oui
Audience :
Internationale
Popular science :
Non
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Source :
Submission date :
2025-01-24T14:31:29Z
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