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On the regularity of the distribution of the maximum of one-parameter Gaussian processes |
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| Authors: | Jean-Marc Azaïs Mario Wschebor |
| Affiliation: | (1) Laboratoire de Statistique et Probabilités, UMR-CNRS C55830, Université Paul Sabatier, 118, route de Narbonne, 31062 Toulouse Cedex 4. France. e-mail: azais@cict.fr, FR;(2) Centro de Matemática, Facultad de Ciencias, Universidad de la República, Calle Igua 4225, 11400 Montevideo, Uruguay. e-mail: wscheb@fcien.edu.uy, UY |
| Abstract: | The main result in this paper states that if a one-parameter Gaussian process has C 2k paths and satisfies a non-degeneracy condition, then the distribution of its maximum on a compact interval is of class C k . 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. Received: 14 May 1999 / Revised version: 18 October 1999 / Published online: 14 December 2000 |
| Keywords: | Mathematics Subject Classification (2000): 60G15 60Gxx 60E05 |
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