Regularity of the distribution of the maximum of a Gaussian process with regular paths

被引：2

作者：

Azaïs, JM

Wschebor, M

机构：

[1] Univ Toulouse 3, Lab Stat & Probabilites, UMR CNRS C55830, F-31062 Toulouse, France

[2] Univ Republica, Fac Ciencias, Ctr Matemat, Montevideo 11400, Uruguay

来源：

COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE | 1999年 / 328卷 / 04期

关键词：

D O I：

10.1016/S0764-4442(99)80220-1

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let X be a real-valued Gaussian process with a one-dimensional parameter If the sample paths of X are of class C-2k, k integer and if the marginal distributions of X and its derivatives have no degeneracy, then the distribution function of the maximum on a bounded interval is of class C-k. We give a recurrence method allowing to express the derivatives by means of certain implicit formulae. (C) Academie des Sciences/Elsevier, Paris.

引用

页码：333 / 336

页数：4

共 50 条

[31] Computing the distribution of the maximum of Gaussian random processes
Cierco-Ayrolles, C
Croquette, A
Delmas, C
[J]. METHODOLOGY AND COMPUTING IN APPLIED PROBABILITY, 2003, 5 (04) : 427 - 438
[32] Computing the Distribution of the Maximum of Gaussian Random Processes
Christine Cierco-Ayrolles
Alain Croquette
Céline Delmas
[J]. Methodology And Computing In Applied Probability, 2003, 5 : 427 - 438
[33] On the distribution of the maximum of a Gaussian field with d parameters
Azaïs, JM
Wschebor, M
[J]. ANNALS OF APPLIED PROBABILITY, 2005, 15 (1A): : 254 - 278
[34] ASYMPTOTIC PROPERTIES OF MAXIMUM IN A STATIONARY GAUSSIAN PROCESS
PICKANDS, J
[J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1969, 145 : 75 - &
[35] Approximate maximum a posteriori with Gaussian process priors
Hegland, Markus
[J]. CONSTRUCTIVE APPROXIMATION, 2007, 26 (02) : 205 - 224
[36] Approximate Maximum a Posteriori with Gaussian Process Priors
Markus Hegland
[J]. Constructive Approximation, 2007, 26 : 205 - 224
[37] REGULARITY OF LIQUID DISTRIBUTION IN REGULAR CORRUGATED GAUZE PACKING LAYERS
KLYKOV, MV
[J]. KHIMICHESKAYA PROMYSHLENNOST, 1984, (03): : 174 - 175
[38] ON THE DISTRIBUTION OF THE MAXIMUM OF THE TELEGRAPH PROCESS
Cinque, F.
Orsingher, E.
[J]. THEORY OF PROBABILITY AND MATHEMATICAL STATISTICS, 2020, 102 : 73 - 95
[39] BV-regularity for the Malliavin derivative of the maximum of a Wiener process
Trevisan, Dario
[J]. ELECTRONIC COMMUNICATIONS IN PROBABILITY, 2013, 18 : 1 - 9
[40] An asymptotic expansion for the distribution of the maximum of a class of Gaussian fields
Delmas, C
[J]. COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 1998, 327 (04): : 393 - 397

← 1 2 3 4 5 →