Probability Theory Exponential Functional of Lévy Processes: Generalized Weierstrass Products and Wiener-hopf Factorization
نویسنده
چکیده
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 the authors in [14] as well as smoothness properties of its distribution. Résumé. Fonctionnelle exponentielle des processus de Lévy : produits de Weierstrass généralisés et factorisation de Wiener-Hopf . 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 les auteurs dans [14] ainsi que des propriétés de régularités pour sa loi.
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