[Une Note sur la régularité du temps des processus Ornstein–Uhlenbeck généralisée avec le bruit stables cylindriques]
Une condition nécessaire et suffisante de la modification càdlàg des processus dʼOrnstein–Uhlenbeck avec bruit stables cylindriques dans un éspace Hilbert est montré dans cette Note. En appliquant ce résultat, quelques questions dans Time irregularity of generalized Ornstein–Uhlenbeck processes [C. R. Acad. Sci. Paris, Ser. I 348 (2010) 273–276] et Structural properties of semilinear SPDEs driven by cylindrical stable process [Probab. Theory Related Fields 149 (2011) 97–137] sont répondues.
A necessary and sufficient condition of càdlàg modification of Ornstein–Uhlenbeck process with cylindrical stable noise in a Hilbert space is given in this Note. Applying this result, some questions in Time irregularity of generalized Ornstein–Uhlenbeck processes [C. R. Acad. Sci. Paris, Ser. I 348 (2010) 273–276] and Structural properties of semilinear SPDEs driven by cylindrical stable process [Probab. Theory Related Fields 149 (2011) 97–137] are answered.
Accepté le :
Publié le :
@article{CRMATH_2012__350_1-2_97_0,
author = {Liu, Yong and Zhai, Jianliang},
title = {A {Note} on time regularity of generalized {Ornstein{\textendash}Uhlenbeck} processes with cylindrical stable noise},
journal = {Comptes Rendus. Math\'ematique},
pages = {97--100},
publisher = {Elsevier},
volume = {350},
number = {1-2},
year = {2012},
doi = {10.1016/j.crma.2011.11.017},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2011.11.017/}
}
TY - JOUR AU - Liu, Yong AU - Zhai, Jianliang TI - A Note on time regularity of generalized Ornstein–Uhlenbeck processes with cylindrical stable noise JO - Comptes Rendus. Mathématique PY - 2012 SP - 97 EP - 100 VL - 350 IS - 1-2 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2011.11.017/ DO - 10.1016/j.crma.2011.11.017 LA - en ID - CRMATH_2012__350_1-2_97_0 ER -
%0 Journal Article %A Liu, Yong %A Zhai, Jianliang %T A Note on time regularity of generalized Ornstein–Uhlenbeck processes with cylindrical stable noise %J Comptes Rendus. Mathématique %D 2012 %P 97-100 %V 350 %N 1-2 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2011.11.017/ %R 10.1016/j.crma.2011.11.017 %G en %F CRMATH_2012__350_1-2_97_0
Liu, Yong; Zhai, Jianliang. A Note on time regularity of generalized Ornstein–Uhlenbeck processes with cylindrical stable noise. Comptes Rendus. Mathématique, Tome 350 (2012) no. 1-2, pp. 97-100. doi : 10.1016/j.crma.2011.11.017. http://www.numdam.org/articles/10.1016/j.crma.2011.11.017/
[1] Time irregularity of generalized Ornstein–Uhlenbeck processes, C. R. Acad. Sci. Paris, Ser. I, Volume 348 (2010), pp. 273-276
[2] Regularity of Ornstein–Uhlenbeck processes driven by Lévy white noise, Potential Anal., Volume 32 (2010), pp. 153-188
[3] Stochastic Processes, John Wiley & Sons Inc., New York, 1953
[4] Generalized Mahler semigroups: the non-Gaussian case, Potential Anal., Volume 12 (2000), pp. 1-47
[5] On the Skorohod topology, Ann. Inst. Henri Poincaré, Volume 22 (1986), pp. 263-285
[6] Stochastic Partial Differential Equations with Lévy Noise, Cambridge University Press, Cambridge, 2007
[7] E. Priola, J. Zabczyk, On linear evolution with cylindrical Lévy noise, in: G. Da Prato, L. Tubaro (Eds.), Stochastic Partial Differential Equations and Applications VIII, Proceedings of the Levico Conference, 2008.
[8] Structural properties of semilinear SPDEs driven by cylindrical stable process, Probab. Theory Related Fields, Volume 149 (2011), pp. 97-137
[9] Lévy Processes and Infinite Divisible Distributions, Cambridge University Press, London, 1999
Cité par Sources :
