Probability Theory
Exponential functional of Lévy processes: Generalized Weierstrass products and Wiener–Hopf factorization
Comptes Rendus. Mathématique, Volume 351 (2013) no. 9-10, pp. 393-396.

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.

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.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2013.04.023
Patie, Pierre 1; Savov, Mladen 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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Patie, Pierre; Savov, Mladen. 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. http://www.numdam.org/articles/10.1016/j.crma.2013.04.023/

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