[Irrégularité en temps des processus Ornstein–Uhlenbeck généralisés]
Dans cette Note on traite les propriétés de solutions d'équations d'évolution linéaires perturbées par des processus de Lévy cylindriques. Sous des conditions assez faibles, on trouve que les solutions ne possèdent pas de modifications càdlàg. On énonce quelques questions naturelles s'en déduisant.
This Note is concerned with the properties of solutions to a linear evolution equation perturbed by a cylindrical Lévy process. It turns out that solutions, under rather weak requirements, do not have a càdlàg modification. Some natural open questions are also stated.
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@article{CRMATH_2010__348_5-6_273_0,
author = {Brze\'zniak, Zdzis{\l}aw and Goldys, Ben and Imkeller, Peter and Peszat, Szymon and Priola, Enrico and Zabczyk, Jerzy},
title = {Time irregularity of generalized {Ornstein{\textendash}Uhlenbeck} processes},
journal = {Comptes Rendus. Math\'ematique},
pages = {273--276},
publisher = {Elsevier},
volume = {348},
number = {5-6},
year = {2010},
doi = {10.1016/j.crma.2010.01.022},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2010.01.022/}
}
TY - JOUR AU - Brzeźniak, Zdzisław AU - Goldys, Ben AU - Imkeller, Peter AU - Peszat, Szymon AU - Priola, Enrico AU - Zabczyk, Jerzy TI - Time irregularity of generalized Ornstein–Uhlenbeck processes JO - Comptes Rendus. Mathématique PY - 2010 SP - 273 EP - 276 VL - 348 IS - 5-6 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2010.01.022/ DO - 10.1016/j.crma.2010.01.022 LA - en ID - CRMATH_2010__348_5-6_273_0 ER -
%0 Journal Article %A Brzeźniak, Zdzisław %A Goldys, Ben %A Imkeller, Peter %A Peszat, Szymon %A Priola, Enrico %A Zabczyk, Jerzy %T Time irregularity of generalized Ornstein–Uhlenbeck processes %J Comptes Rendus. Mathématique %D 2010 %P 273-276 %V 348 %N 5-6 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2010.01.022/ %R 10.1016/j.crma.2010.01.022 %G en %F CRMATH_2010__348_5-6_273_0
Brzeźniak, Zdzisław; Goldys, Ben; Imkeller, Peter; Peszat, Szymon; Priola, Enrico; Zabczyk, Jerzy. Time irregularity of generalized Ornstein–Uhlenbeck processes. Comptes Rendus. Mathématique, Tome 348 (2010) no. 5-6, pp. 273-276. doi : 10.1016/j.crma.2010.01.022. http://www.numdam.org/articles/10.1016/j.crma.2010.01.022/
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☆ Supported by the Polish Ministry of Science and Education project 1PO 3A 034 29 “Stochastic evolution equations with Lévy noise” and by EC FP6 Marie Curie ToK programme SPADE2.
