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

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.

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 .

DOI : 10.1214/12-AIHP497
Classification : 60G17, 60G51, 60G52, 60G44
Mots clés : Lévy processes, stable Lévy processes, reflected processes, penalisation, path decomposition, conditioning to stay negative/positive, conditioning to hit $0$ continuously
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Yano, Yuko. A remarkable $\sigma $-finite measure unifying supremum penalisations for a stable Lévy process. Annales de l'I.H.P. Probabilités et statistiques, Tome 49 (2013) no. 4, pp. 1014-1032. doi : 10.1214/12-AIHP497. http://www.numdam.org/articles/10.1214/12-AIHP497/

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