On the regularity of the distribution of the maximum of one-parameter Gaussian processes
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 derivative...
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| Veröffentlicht in: | Probability theory and related fields 2001, Vol.119 (1), p.70-98 |
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| container_title | Probability theory and related fields |
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| creator | AZAÏS, Jean-Marc WSCHEBOR, Mario |
| description | 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. |
| doi_str_mv | 10.1007/PL00012739 |
| format | Article |
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| identifier | ISSN: 0178-8051 |
| ispartof | Probability theory and related fields, 2001, Vol.119 (1), p.70-98 |
| issn | 0178-8051 1432-2064 |
| language | eng |
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| source | Business Source Complete; SpringerLink Journals - AutoHoldings |
| subjects | Asymptotic properties Distribution theory Exact sciences and technology Gaussian process Mathematics Probability Probability and statistics Probability theory and stochastic processes Process parameters Sciences and techniques of general use Stochastic processes |
| title | On the regularity of the distribution of the maximum of one-parameter Gaussian processes |
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