[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 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.
Accepté le :
Publié le :
Pierre Patie 1 ; Mladen Savov 2
@article{CRMATH_2013__351_9-10_393_0, author = {Pierre Patie and Mladen Savov}, title = {Exponential functional of {L\'evy} processes: {Generalized} {Weierstrass} products and {Wiener{\textendash}Hopf} factorization}, journal = {Comptes Rendus. Math\'ematique}, pages = {393--396}, publisher = {Elsevier}, volume = {351}, number = {9-10}, year = {2013}, doi = {10.1016/j.crma.2013.04.023}, language = {en}, }
TY - JOUR AU - Pierre Patie AU - Mladen Savov TI - Exponential functional of Lévy processes: Generalized Weierstrass products and Wiener–Hopf factorization JO - Comptes Rendus. Mathématique PY - 2013 SP - 393 EP - 396 VL - 351 IS - 9-10 PB - Elsevier DO - 10.1016/j.crma.2013.04.023 LA - en ID - CRMATH_2013__351_9-10_393_0 ER -
%0 Journal Article %A Pierre Patie %A Mladen Savov %T Exponential functional of Lévy processes: Generalized Weierstrass products and Wiener–Hopf factorization %J Comptes Rendus. Mathématique %D 2013 %P 393-396 %V 351 %N 9-10 %I Elsevier %R 10.1016/j.crma.2013.04.023 %G en %F CRMATH_2013__351_9-10_393_0
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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