Penalisation of a stable Lévy process involving its one-sided supremum
Yano, Kouji ; Yano, Yuko ; Yor, Marc
Annales de l'I.H.P. Probabilités et statistiques, Tome 46 (2010), p. 1042-1054 / Harvested from Numdam
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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.

Publié le : 2010-01-01
DOI : https://doi.org/10.1214/09-AIHP339
Classification:  60B10,  60G52,  60G44 
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     title = {Penalisation of a stable L\'evy process involving its one-sided supremum},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     volume = {46},
     year = {2010},
     pages = {1042-1054},
     doi = {10.1214/09-AIHP339},
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     zbl = {1208.60046},
     language = {en},
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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) pp. 1042-1054. doi : 10.1214/09-AIHP339. http://gdmltest.u-ga.fr/item/AIHPB_2010__46_4_1042_0/

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