Title :

Hitting densities for spectrally positive stable processes

Author(s) :

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

English keyword(s) :

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

HAL domain(s) :

Mathématiques [math]/Probabilités [math.PR]

English abstract : [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 ...
Show more >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.Show less >

Language :

Anglais

ANR Project :

Etude de certains processus autosimilaires et applications

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL