Statistics/Probability Theory
Tail behavior of anisotropic norms for Gaussian random fields
[Comportement des queues pour les normes anisotropes des champs aléatoires gaussiens]
Comptes Rendus. Mathématique, Tome 336 (2003) no. 1, pp. 85-88.

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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Accepté le :
Publié le :
DOI : 10.1016/S1631-073X(02)00013-4
Lifshits, Mikhail 1 ; Nazarov, Alexander 1 ; Nikitin, Yakov 1

1 Department of Mathematics and Mechanics, St. Petersburg State University, St. Petersburg 198504, Russia
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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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