A remarkable $\sigma$-finite measure unifying supremum penalisations for a stable Lévy process

Yano, Yuko

Annales de l'I.H.P. Probabilités et statistiques, Tome 49 (2013) no. 4, pp. 1014-1032.

On introduit la mesure $\sigma$-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 $\sigma$-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 ${𝒫}_{sup}$.

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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