A remarkable σ-finite measure unifying supremum penalisations for a stable Lévy process
Annales de l'I.H.P. Probabilités et statistiques, Volume 49 (2013) no. 4, p. 1014-1032

The σ-finite measure 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 𝒫 sup .

On introduit la mesure σ-finie 𝒫 sup , unifiant les pénalisations selon le supremum pour un processus de Lévy stable. Dans la construction de 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.

DOI : https://doi.org/10.1214/12-AIHP497
Classification:  60G17,  60G51,  60G52,  60G44
Keywords: Lévy processes, stable Lévy processes, reflected processes, penalisation, path decomposition, conditioning to stay negative/positive, conditioning to hit 0 continuously
@article{AIHPB_2013__49_4_1014_0,
     author = {Yano, Yuko},
     title = {A remarkable $\sigma $-finite measure unifying supremum penalisations for a stable L\'evy process},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     publisher = {Gauthier-Villars},
     volume = {49},
     number = {4},
     year = {2013},
     pages = {1014-1032},
     doi = {10.1214/12-AIHP497},
     zbl = {1282.60051},
     mrnumber = {3127911},
     language = {en},
     url = {http://www.numdam.org/item/AIHPB_2013__49_4_1014_0}
}
Yano, Yuko. A remarkable $\sigma $-finite measure unifying supremum penalisations for a stable Lévy process. Annales de l'I.H.P. Probabilités et statistiques, Volume 49 (2013) no. 4, pp. 1014-1032. doi : 10.1214/12-AIHP497. http://www.numdam.org/item/AIHPB_2013__49_4_1014_0/

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