[Une classe de processus multifractals semi-stables contenant subordinateurs de Lévy et cascades multiplicatives de Mandelbrot]
Nous présentons une classe de processus auto-similaires en loi naturellement associés aux généralisations des lois semi-stables considérées. Cette classe contient en particulier les subordinateurs stables de Lévy ainsi que les cascades multiplicatives de Mandelbrot ; ses éléments sont des cas particuliers des processus de Lévy en temps multifractal étudiés ailleurs. Nous étudions leur nature multifractale.
We exhibit a class of statistically self-similar processes naturally associated with the so-called fixed points of the smoothing transformation. This class includes stable subordinators and Mandelbrot multiplicative cascades. Both these processes are special examples of Lévy processes in multifractal time, which are studied in other works. We describe their multifractal nature.
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@article{CRMATH_2005__341_9_579_0,
author = {Julien Barral and St\'ephane Seuret},
title = {A class of multifractal semi-stable processes including {L\'evy} subordinators and {Mandelbrot} multiplicative cascades},
journal = {Comptes Rendus. Math\'ematique},
pages = {579--582},
publisher = {Elsevier},
volume = {341},
number = {9},
year = {2005},
doi = {10.1016/j.crma.2005.09.020},
language = {en},
}
TY - JOUR AU - Julien Barral AU - Stéphane Seuret TI - A class of multifractal semi-stable processes including Lévy subordinators and Mandelbrot multiplicative cascades JO - Comptes Rendus. Mathématique PY - 2005 SP - 579 EP - 582 VL - 341 IS - 9 PB - Elsevier DO - 10.1016/j.crma.2005.09.020 LA - en ID - CRMATH_2005__341_9_579_0 ER -
%0 Journal Article %A Julien Barral %A Stéphane Seuret %T A class of multifractal semi-stable processes including Lévy subordinators and Mandelbrot multiplicative cascades %J Comptes Rendus. Mathématique %D 2005 %P 579-582 %V 341 %N 9 %I Elsevier %R 10.1016/j.crma.2005.09.020 %G en %F CRMATH_2005__341_9_579_0
Julien Barral; Stéphane Seuret. A class of multifractal semi-stable processes including Lévy subordinators and Mandelbrot multiplicative cascades. Comptes Rendus. Mathématique, Volume 341 (2005) no. 9, pp. 579-582. doi : 10.1016/j.crma.2005.09.020. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2005.09.020/
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