[Comportement des queues pour les normes anisotropes des champs aléatoires gaussiens]
Nous étudions les grandes déviations logarithmiques pour les normes anisotropes des champs gaussiens aléatoires de deux variables. Le problème est résolu en calculant des normes anisotropes pour les opérateurs intégraux engendrés par les covariances. Nous trouvons des valeurs exactes de telles normes pour quelques classes importantes de champs gaussiens.
We investigate the logarithmic large deviation asymptotics for anisotropic norms of Gaussian random functions of two variables. The problem is solved by the evaluation of the anisotropic norms of corresponding integral covariance operators. We find the exact values of such norms for some important classes of Gaussian fields.
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@article{CRMATH_2003__336_1_85_0,
author = {Lifshits, Mikhail and Nazarov, Alexander and Nikitin, Yakov},
title = {Tail behavior of anisotropic norms for {Gaussian} random fields},
journal = {Comptes Rendus. Math\'ematique},
pages = {85--88},
publisher = {Elsevier},
volume = {336},
number = {1},
year = {2003},
doi = {10.1016/S1631-073X(02)00013-4},
language = {en},
url = {http://www.numdam.org/articles/10.1016/S1631-073X(02)00013-4/}
}
TY - JOUR AU - Lifshits, Mikhail AU - Nazarov, Alexander AU - Nikitin, Yakov TI - Tail behavior of anisotropic norms for Gaussian random fields JO - Comptes Rendus. Mathématique PY - 2003 SP - 85 EP - 88 VL - 336 IS - 1 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/S1631-073X(02)00013-4/ DO - 10.1016/S1631-073X(02)00013-4 LA - en ID - CRMATH_2003__336_1_85_0 ER -
%0 Journal Article %A Lifshits, Mikhail %A Nazarov, Alexander %A Nikitin, Yakov %T Tail behavior of anisotropic norms for Gaussian random fields %J Comptes Rendus. Mathématique %D 2003 %P 85-88 %V 336 %N 1 %I Elsevier %U http://www.numdam.org/articles/10.1016/S1631-073X(02)00013-4/ %R 10.1016/S1631-073X(02)00013-4 %G en %F CRMATH_2003__336_1_85_0
Lifshits, Mikhail; Nazarov, Alexander; Nikitin, Yakov. Tail behavior of anisotropic norms for Gaussian random fields. Comptes Rendus. Mathématique, Tome 336 (2003) no. 1, pp. 85-88. doi : 10.1016/S1631-073X(02)00013-4. http://www.numdam.org/articles/10.1016/S1631-073X(02)00013-4/
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