Comptes Rendus
no. 1
Statistics/Probability Theory
Tail behavior of anisotropic norms for Gaussian random fields
[Comportement des queues pour les normes anisotropes des champs aléatoires gaussiens]

Présenté par : Paul Deheuvels

Mikhail Lifshits1 ; Alexander Nazarov1 ; Yakov Nikitin1
1 Department of Mathematics and Mechanics, St. Petersburg State University, St. Petersburg 198504, Russia
Comptes Rendus. Mathématique, Volume 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.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/S1631-073X(02)00013-4

Mikhail Lifshits 1 ; Alexander Nazarov 1 ; Yakov Nikitin 1

1 Department of Mathematics and Mechanics, St. Petersburg State University, St. Petersburg 198504, Russia 
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Mikhail Lifshits; Alexander Nazarov; Yakov Nikitin. Tail behavior of anisotropic norms for Gaussian random fields. Comptes Rendus. Mathématique, Volume 336 (2003) no. 1, pp. 85-88. doi : 10.1016/S1631-073X(02)00013-4. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(02)00013-4/

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