Annales de l'Institut Henri Poincaré, Probabilités et Statistiques

A remarkable $\sigma$-finite measure unifying supremum penalisations for a stable Lévy process

Yuko Yano

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Abstract

The $\sigma$-finite measure $\mathcal{P} _{\sup}$ which unifies supremum penalisations for a stable Lévy process is introduced. Silverstein’s coinvariant and coharmonic functions for Lévy processes and Chaumont’s $h$-transform processes with respect to these functions are utilized for the construction of $\mathcal{P} _{\sup}$.

Résumé

On introduit la mesure $\sigma$-finie $\mathcal{P} _{\sup}$, unifiant les pénalisations selon le supremum pour un processus de Lévy stable. Dans la construction de $\mathcal{P} _{\sup}$ on utilise les fonctions co-invariantes et co-harmoniques de Silverstein pour les processus de Lévy, et les processus $h$-transformés par rapport à ces fonctions selon l’approche de Chaumont.

Article information

Source
Ann. Inst. H. Poincaré Probab. Statist., Volume 49, Number 4 (2013), 1014-1032.

Dates
First available in Project Euclid: 2 October 2013

Permanent link to this document
https://projecteuclid.org/euclid.aihp/1380718735

Digital Object Identifier
doi:10.1214/12-AIHP497

Mathematical Reviews number (MathSciNet)
MR3127911

Zentralblatt MATH identifier
1282.60051

Subjects
Primary: 60G17: Sample path properties
Secondary: 60G51: Processes with independent increments; Lévy processes 60G52: Stable processes 60G44: Martingales with continuous parameter

Keywords
Lévy processes Stable Lévy processes Reflected processes Penalisation Path decomposition Conditioning to stay negative/positive Conditioning to hit $0$ continuously

Citation

Yano, Yuko. A remarkable $\sigma$-finite measure unifying supremum penalisations for a stable Lévy process. Ann. Inst. H. Poincaré Probab. Statist. 49 (2013), no. 4, 1014--1032. doi:10.1214/12-AIHP497. https://projecteuclid.org/euclid.aihp/1380718735


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