Titre :

Hitting densities for spectrally positive stable processes

Auteur(s) :

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

Mot(s)-clé(s) en anglais :

Exit time
Hitting time
Mellin transform
Running supremum
Series representation
Stable Lévy processes
Unimodality

Discipline(s) HAL :

Mathématiques [math]/Probabilités [math.PR]

Résumé en anglais : [en]

A multiplicative identity in law connecting the hitting times of completely asymmetric $\alpha-$stable Lévy processes in duality is established. In the spectrally positive case, this identity allows with an elementary ...
Lire la suite >A multiplicative identity in law connecting the hitting times of completely asymmetric $\alpha-$stable Lévy processes in duality is established. In the spectrally positive case, this identity allows with an elementary argument to compute fractional moments and to get series representations for the density. We also prove that the hitting times are unimodal as soon as $\alpha\le 3/2.$ Analogous results are obtained, in a much simplified manner, for the first passage time across a positive level.Lire moins >

Langue :

Anglais

Projet ANR :

Etude de certains processus autosimilaires et applications

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL