On the regularity of the distribution of the maximum of one-parameter Gaussian processes

被引：0
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作者：
Jean-Marc Azaïs
Mario Wschebor
机构：
[1] Laboratoire de Statistique et Probabilités,
[2] UMR-CNRS C55830,undefined
[3] Université Paul Sabatier,undefined
[4] 118,undefined
[5] route de Narbonne,undefined
[6] 31062 Toulouse Cedex 4. France. e-mail: azais@cict.fr,undefined
[7] Centro de Matemática,undefined
[8] Facultad de Ciencias,undefined
[9] Universidad de la República,undefined
[10] Calle Igua 4225,undefined
[11] 11400 Montevideo,undefined
[12] Uruguay. e-mail: wscheb@fcien.edu.uy,undefined
来源：
Probability Theory and Related Fields | 2001年 / 119卷
关键词：
Mathematics Subject Classification (2000): 60G15, 60Gxx, 60E05; Key words or phrases: Extreme values – Distribution of the maximum;
D O I：
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学科分类号：
摘要：
The main result in this paper states that if a one-parameter Gaussian process has C2k paths and satisfies a non-degeneracy condition, then the distribution of its maximum on a compact interval is of class Ck. The methods leading to this theorem permit also to give bounds on the successive derivatives of the distribution of the maximum and to study their asymptotic behaviour as the level tends to infinity.
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页码：70 / 98
页数：28
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