Title :

The area of a spectrally positive stable process stopped at zero

Author(s) :

Letemplier, Julien [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Simon, Thomas [Auteur]
Laboratoire de Physique Théorique et Modèles Statistiques [LPTMS]
Laboratoire Paul Painlevé - UMR 8524 [LPP]

English keyword(s) :

Exponential functional
Hitting time
Integrated process
Moments of Gamma type
Self-decomposability
Series representation
Stable Lévy process

HAL domain(s) :

Mathématiques [math]/Probabilités [math.PR]

English abstract : [en]

An identity in law for the area of a spectrally positive Lévy stable process stopped at zero is established. Extending that of Lefebvre for Brownian motion, it involves an inverse Beta random variable and the square of a ...
Show more >An identity in law for the area of a spectrally positive Lévy stable process stopped at zero is established. Extending that of Lefebvre for Brownian motion, it involves an inverse Beta random variable and the square of a positive stable random variable. This identity entails that the stopped area is distributed as the perpetuity of a spectrally negative Lévy process, and is hence self-decomposable. We also derive a convergent series representation for the density, whose behaviour at zero is shown to be Fréchet-like.Show less >

Language :

Anglais

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL