Title :

On the harmonic measure of stable processes

Author(s) :

Profeta, Christophe [Auteur]
Laboratoire de Mathématiques et Modélisation d'Evry [LaMME]
Simon, Thomas [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Laboratoire de Physique Théorique et Modèles Statistiques [LPTMS]

Journal title :

Séminaire de Probabilités

Pages :

325-345

Publisher :

Springer-Verlag

Publication date :

2016

ISSN :

0720-8766

English keyword(s) :

Martin kernel
Stable L\'evy process
Hypergeometric function
Hitting probability
Green function
Harmonic measure

HAL domain(s) :

Mathématiques [math]/Probabilités [math.PR]

English abstract : [en]

Using three hypergeometric identities, we evaluate the harmonic measure of a finite interval and of its complementary for a strictly stable real Lévy process. This gives a simple and unified proof of several results in the ...
Show more >Using three hypergeometric identities, we evaluate the harmonic measure of a finite interval and of its complementary for a strictly stable real Lévy process. This gives a simple and unified proof of several results in the literature, old and recent. We also provide a full description of the corresponding Green functions. As a by-product, we compute the hitting probabilities of points and describe the non-negative harmonic functions for the stable process killed outside a finite interval.Show less >

Language :

Anglais

Popular science :

Non

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL