Annales de l'Institut Henri Poincaré, Probabilités et Statistiques

Penalisation of a stable Lévy process involving its one-sided supremum

Kouji Yano, Yuko Yano, and Marc Yor

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Abstract

Penalisation involving the one-sided supremum for a stable Lévy process with index α∈(0, 2] is studied. We introduce the analogue of Azéma–Yor martingales for a stable Lévy process and give the law of the overall supremum under the penalised measure.

Résumé

On étudie des pénalisations d’un processus de Lévy stable d’indice α∈(0, 2] qui font intervenir son supremum unilatéral. On introduit pour un processus de Lévy stable, des martingales analogues aux martingales d’Azéma–Yor pour le mouvement brownien et son supremum; ceci permet d’obtenir la loi du supremum global relativement à la mesure pénalisée.

Article information

Source
Ann. Inst. H. Poincaré Probab. Statist., Volume 46, Number 4 (2010), 1042-1054.

Dates
First available in Project Euclid: 4 November 2010

Permanent link to this document
https://projecteuclid.org/euclid.aihp/1288878337

Digital Object Identifier
doi:10.1214/09-AIHP339

Mathematical Reviews number (MathSciNet)
MR2744885

Zentralblatt MATH identifier
1208.60046

Subjects
Primary: 60B10: Convergence of probability measures
Secondary: 60G52: Stable processes 60G44: Martingales with continuous parameter

Keywords
Stable Lévy processes Reflected Lévy processes Penalisation

Citation

Yano, Kouji; Yano, Yuko; Yor, Marc. Penalisation of a stable Lévy process involving its one-sided supremum. Ann. Inst. H. Poincaré Probab. Statist. 46 (2010), no. 4, 1042--1054. doi:10.1214/09-AIHP339. https://projecteuclid.org/euclid.aihp/1288878337


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