[Approximation de la mesure d'occupation d'un processus de Lévy]
On considère un processus de Lévy à valeurs réelles, dont la partie gaussienne ne s'annule pas et dont la variation totale des sauts est localement finie. Nous donnons un théorème central limite pour la vitesse d'approximation de sa mesure d'occupation, moyennant des fonctionnelles définies sur des régularisations des trajectoires. Ce théorème est une première extension à des processus avec sauts, de résultats précédents obtenus pour des semi-martingales à trajectoires continues.
Consider a real-valued Lévy process with non-zero Gaussian component and jumps with locally finite variation. We obtain an invariance principle theorem for the speed of approximation of its occupation measure by means of functionals defined on regularizations of the paths. This theorem is a first extension to processes with jumps of previous results for semimartingales with continuous paths.
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@article{CRMATH_2005__340_8_605_0,
author = {Mordecki, Ernesto and Wschebor, Mario},
title = {Approximation of the occupation measure of {L\'evy} processes},
journal = {Comptes Rendus. Math\'ematique},
pages = {605--610},
publisher = {Elsevier},
volume = {340},
number = {8},
year = {2005},
doi = {10.1016/j.crma.2005.03.005},
language = {en},
url = {http://archive.numdam.org/articles/10.1016/j.crma.2005.03.005/}
}
TY - JOUR AU - Mordecki, Ernesto AU - Wschebor, Mario TI - Approximation of the occupation measure of Lévy processes JO - Comptes Rendus. Mathématique PY - 2005 SP - 605 EP - 610 VL - 340 IS - 8 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.crma.2005.03.005/ DO - 10.1016/j.crma.2005.03.005 LA - en ID - CRMATH_2005__340_8_605_0 ER -
%0 Journal Article %A Mordecki, Ernesto %A Wschebor, Mario %T Approximation of the occupation measure of Lévy processes %J Comptes Rendus. Mathématique %D 2005 %P 605-610 %V 340 %N 8 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.crma.2005.03.005/ %R 10.1016/j.crma.2005.03.005 %G en %F CRMATH_2005__340_8_605_0
Mordecki, Ernesto; Wschebor, Mario. Approximation of the occupation measure of Lévy processes. Comptes Rendus. Mathématique, Tome 340 (2005) no. 8, pp. 605-610. doi : 10.1016/j.crma.2005.03.005. http://archive.numdam.org/articles/10.1016/j.crma.2005.03.005/
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