Open Access
Translator Disclaimer
May 2019 Exponential functionals of spectrally one-sided Lévy processes conditioned to stay positive
Grégoire Véchambre
Ann. Inst. H. Poincaré Probab. Statist. 55(2): 620-660 (May 2019). DOI: 10.1214/18-AIHP892

Abstract

We study the properties of the exponential functional $\int_{0}^{+\infty }e^{-X^{\uparrow }(t)}\,dt$ where $X^{\uparrow }$ is a spectrally one-sided Lévy process conditioned to stay positive. In particular, we study finiteness, self-decomposability, existence of finite exponential moments, asymptotic tail at $0$ and smoothness of the density.

On étudie les propriétés de la fonctionnelle exponentielle $\int_{0}^{+\infty }e^{-X^{\uparrow }(t)}\,dt$ où $X^{\uparrow }$ est un processus de Lévy spectralement positifs ou négatifs conditionné à rester positif. On étudie en particulier la finitude, l’auto-décomposabilité, l’existence de moments exponentiels finis, la queue de distribution en 0 et la régularité de la densité.

Citation

Download Citation

Grégoire Véchambre. "Exponential functionals of spectrally one-sided Lévy processes conditioned to stay positive." Ann. Inst. H. Poincaré Probab. Statist. 55 (2) 620 - 660, May 2019. https://doi.org/10.1214/18-AIHP892

Information

Received: 17 July 2015; Revised: 12 February 2018; Accepted: 13 February 2018; Published: May 2019
First available in Project Euclid: 14 May 2019

zbMATH: 07097326
MathSciNet: MR3949948
Digital Object Identifier: 10.1214/18-AIHP892

Subjects:
Primary: 60G51

Keywords: Exponential functionals , Lévy processes conditioned to stay positive , Self-decomposable distributions

Rights: Copyright © 2019 Institut Henri Poincaré

JOURNAL ARTICLE
41 PAGES


SHARE
Vol.55 • No. 2 • May 2019
Back to Top