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.
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.
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Mikhail Lifshits 1; Alexander Nazarov 1; Yakov Nikitin 1
@article{CRMATH_2003__336_1_85_0, author = {Mikhail Lifshits and Alexander Nazarov and Yakov Nikitin}, 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}, }
TY - JOUR AU - Mikhail Lifshits AU - Alexander Nazarov AU - Yakov Nikitin 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 DO - 10.1016/S1631-073X(02)00013-4 LA - en ID - CRMATH_2003__336_1_85_0 ER -
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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