Comptes Rendus
no. 9-10
Probability Theory
Exponential functional of Lévy processes: Generalized Weierstrass products and Wiener–Hopf factorization
[Fonctionnelle exponentielle des processus de Lévy : produits de Weierstrass généralisés et factorisation de Wiener–Hopf]

Présenté par : the Editorial Board

Pierre Patie1 ; Mladen Savov2
1 School of Operations Research and Information Engineering, Cornell University, Ithaca, NY 14853, USA
2 University of Reading, Department of Mathematics and Statistics, Whiteknights, PO Box 220, Reading RG6 6AX, UK
Comptes Rendus. Mathématique, Volume 351 (2013) no. 9-10, pp. 393-396.

Dans cette note, nous énonçons une représentation de la transformée de Mellin de la fonctionnelle exponentielle des processus de Lévy sous la forme de produits de Weierstrass généralisés. Nous en déduisons une factorisation multiplicative de Wiener–Hopf généralisant un résultat obtenu récemment par Patie et Savov (2012) [14] ainsi que des propriétés de régularité pour sa loi.

In this note, we state a representation of the Mellin transform of the exponential functional of Lévy processes in terms of generalized Weierstrass products. As by-product, we obtain a multiplicative Wiener–Hopf factorization generalizing previous results obtained by Patie and Savov (2012) [14] as well as smoothness properties of its distribution.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2013.04.023

Pierre Patie 1 ; Mladen Savov 2

1 School of Operations Research and Information Engineering, Cornell University, Ithaca, NY 14853, USA
2 University of Reading, Department of Mathematics and Statistics, Whiteknights, PO Box 220, Reading RG6 6AX, UK 
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Pierre Patie; Mladen Savov. Exponential functional of Lévy processes: Generalized Weierstrass products and Wiener–Hopf factorization. Comptes Rendus. Mathématique, Volume 351 (2013) no. 9-10, pp. 393-396. doi : 10.1016/j.crma.2013.04.023. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2013.04.023/

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