An asymptotic expansion for the distribution of the maximum of a class of Gaussian fields;Un développement asymptotique pour la distribution du maximum d'une classe de champs gaussiens

Comptes Rendus de l'Academie des Sciences - Series I: Mathematics

Volumn 327, Issue 4, 1998, Pages 393-397

  Delmas, Céline ^a  

^a INSTITUT DE MATHÉMATIQUES DE TOULOUSE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0032135527     PISSN: 07644442     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0764-4442(99)80055-X     Document Type: Article

References (10)

1. [1] Adler R.J., The Geometry of Random Fields, Wiley, New York, 1981.
2. [2] Adler R.J., An Introduction to Continuity, Extrema and Related Topics for General Gaussian Processes, IMS, Hayward, CA, 1990.
3. [3] Azaïs J.-M., Wschebor M., Une formule pour calculer la distribution du maximum d'un processus stochastique, C. R. Acad. Sci. Paris 324 série 1 (1997) 225-230.
4. [4] Azaïs, J.-M., Wschebor, M., The Distribution of the Maximum of a Stochastic Process and the Rice Method, Preprint, 1998.
5. [5] Cramer H., Leadbetter M.R., Stationary and Related Stochastic Processes, J. Wiley & Sons, New York, 1967.
6. [6] Hasofer A.M., The Mean Number of Maxima Above High Levels in Gaussian Random Fields, J. Appl. Probab. 13 (1976) 377-379.
7. [7] Piterbarg V.I., Comparison of Distribution Functions of Maxima of Gaussian Processes, Th. Probab. Appl. 26 (1981) 687-705.
8. [8] Piterbarg V.I., Rice's Method for Large Excursions of Gaussian Random Fields, Technical Report No. 478, University of North-Carolina, Translation of Rice's method for Gaussian random fields, Fund. Appl. Math. 2 (1996) 187-204 (in Russian).
9. [9] Sun J., Significance levels in exploratory projection pursuit, Biometrika 78 (1991) 759-769.
10. [10] Sun J., Tail Probabilities of the Maxima of Gaussian Random Fields, Ann. Probab. 21 (1993) 34-71.