Annales de l'Institut Henri Poincaré, Probabilités et Statistiques

Exponential functionals of spectrally one-sided Lévy processes conditioned to stay positive

Grégoire Véchambre

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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.

Résumé

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.

Article information

Source
Ann. Inst. H. Poincaré Probab. Statist., Volume 55, Number 2 (2019), 620-660.

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

Permanent link to this document
https://projecteuclid.org/euclid.aihp/1557820826

Digital Object Identifier
doi:10.1214/18-AIHP892

Mathematical Reviews number (MathSciNet)
MR3949948

Zentralblatt MATH identifier
07097326

Subjects
Primary: 60G51: Processes with independent increments; Lévy processes

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

Citation

Véchambre, Grégoire. Exponential functionals of spectrally one-sided Lévy processes conditioned to stay positive. Ann. Inst. H. Poincaré Probab. Statist. 55 (2019), no. 2, 620--660. doi:10.1214/18-AIHP892. https://projecteuclid.org/euclid.aihp/1557820826


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