Central limit theorem for wave-functionals of Gaussian processes

被引：4

作者：

Piterbarg, V ^{[1
]}

Rychlik, I

机构：

[1] Moscow MV Lomonosov State Univ, Fac Mech & Math, Moscow 119899, Russia

[2] Univ Lund, Ctr Math Sci, S-22100 Lund, Sweden

来源：

ADVANCES IN APPLIED PROBABILITY | 1999年 / 31卷 / 01期

关键词：

crossings; Slepian models; strong mixing property; central limit theorem;

D O I：

10.1017/S0001867800009009

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

In this paper a central limit theorem is proved for wave-functionals defined as the sums of wave amplitudes observed in sample paths of stationary continuously differentiable Gaussian processes. Examples illustrating this theory are given. AMS 1991 Subject Classification: Primary 60G15; 60G35 Secondary 60K40; 60F05.

引用

页码：158 / 177

页数：20

共 50 条

[31] A Central Limit Theorem for Almost Local Additive Tree Functionals
Dimbinaina Ralaivaosaona
Matas Šileikis
Stephan Wagner
[J]. Algorithmica, 2020, 82 : 642 - 679
[32] Central limit theorems for functionals of linear processes and their applications
Wu, WB
[J]. STATISTICA SINICA, 2002, 12 (02) : 635 - 649
[33] Central limit theorem for the local time of a Gaussian process
Ben Hariz, S
Doukhan, P
León, JR
[J]. SEMINAR ON STOCHASTIC ANALYSIS, RANDOM FIELDS AND APPLICATIONS, 1999, 45 : 25 - 37
[34] EXTREME VALUES AND A GAUSSIAN CENTRAL-LIMIT-THEOREM
KUELBS, J
LEDOUX, M
[J]. PROBABILITY THEORY AND RELATED FIELDS, 1987, 74 (03) : 341 - 355
[35] A CENTRAL-LIMIT-THEOREM FOR CUMULATIVE PROCESSES
ROGINSKY, AL
[J]. ADVANCES IN APPLIED PROBABILITY, 1994, 26 (01) : 104 - 121
[36] A CLASS OF STATIONARY PROCESSES AND A CENTRAL LIMIT THEOREM
BLUM, JR
ROSENBLATT, M
[J]. DUKE MATHEMATICAL JOURNAL, 1957, 24 (01) : 73 - 78
[37] CENTRAL LIMIT THEOREM FOR SAMPLE CONTINUOUS PROCESSES
GINEM, E
[J]. ANNALS OF PROBABILITY, 1974, 2 (04): : 629 - 641
[38] Central limit theorem for stationary linear processes
Peligrad, Magda
Utev, Sergey
[J]. ANNALS OF PROBABILITY, 2006, 34 (04): : 1608 - 1622
[39] GORDINS CENTRAL LIMIT THEOREM FOR STATIONARY PROCESSES
EAGLESON, GK
[J]. JOURNAL OF APPLIED PROBABILITY, 1975, 12 (01) : 176 - 179
[40] On the functional central limit theorem for stationary processes
Dedecker, J
Rio, E
[J]. ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES, 2000, 36 (01): : 1 - 34

← 1 2 3 4 5 →