| Автор | Azaïs, Jean-Marc |
| Автор | Cierco-Ayrolles, Christine |
| Автор | Croquette, Alain |
| Дата выпуска | 1999 |
| dc.description | This paper uses the Rice method [18] to give bounds to the distribution of the maximum of a smooth stationary Gaussian process. We give simpler expressions of the first two terms of the Rice series [3,13] for the distribution of the maximum. Our main contribution is a simpler form of the second factorial moment of the number of upcrossings which is in some sense a generalization of Steinberg et al.'s formula ([7] p. 212). Then, we present a numerical application and asymptotic expansions that give a new interpretation of a result by Piterbarg [15]. |
| Формат | application.pdf |
| Издатель | EDP Sciences |
| Копирайт | © EDP Sciences, SMAI, 1999 |
| Тема | Asymptotic expansions |
| Тема | extreme values |
| Тема | stationary Gaussian process |
| Тема | Rice series |
| Тема | upcrossings. |
| Название | Bounds and asymptotic expansions for the distribution of the Maximum of a smooth stationary Gaussian process |
| Тип | research-article |
| DOI | 10.1051/ps:1999105 |
| Electronic ISSN | 1262-3318 |
| Print ISSN | 1292-8100 |
| Журнал | ESAIM: Probability and Statistics |
| Том | 3 |
| Первая страница | 107 |
| Последняя страница | 129 |
| Аффилиация | Azaïs Jean-Marc; Laboratoire de Statistique et Probabilités, UMR C55830 du CNRS, Université Paul Sabatier, 118 route de Narbonne, 31062 Toulouse Cedex 4, France. |
| Аффилиация | Cierco-Ayrolles Christine; Institut National de la Recherche Agronomique, Unité de Biométrie et Intelligence Artificielle, BP. 27, Chemin de Borde-Rouge, 31326 Castanet-Tolosan Cedex, France.; Laboratoire de Statistique et Probabilités, UMR C55830 du CNRS, Université Paul Sabatier, 118 route de Narbonne, 31062 Toulouse Cedex 4, France. |
| Аффилиация | Croquette Alain; Laboratoire de Statistique et Probabilités, UMR C55830 du CNRS, Université Paul Sabatier, 118 route de Narbonne, 31062 Toulouse Cedex 4, France. |
