Penalisation of a stable Lévy process involving its one-sided supremum
Annales de l'I.H.P. Probabilités et statistiques, Tome 46 (2010) no. 4, pp. 1042-1054.

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.

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.

DOI : 10.1214/09-AIHP339
Classification : 60B10, 60G52, 60G44
Mots-clés : stable Lévy processes, reflected Lévy processes, penalisation 
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Yano, Kouji; Yano, Yuko; Yor, Marc. Penalisation of a stable Lévy process involving its one-sided supremum. Annales de l'I.H.P. Probabilités et statistiques, Tome 46 (2010) no. 4, pp. 1042-1054. doi : 10.1214/09-AIHP339. http://www.numdam.org/articles/10.1214/09-AIHP339/

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