Invariance principle, multifractional Gaussian processes and long-range dependence

被引：9

作者：

Cohen, Serge ^{[1
]}

Marty, Renaud ^{[2
]}

机构：

[1] Univ Toulouse 3, Lab Stat & Probabilites, F-31062 Toulouse 4, France

[2] Univ Calif Irvine, Dept Math, Irvine, CA 92697 USA

来源：

ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES | 2008年 / 44卷 / 03期

关键词：

invariance principle; long range dependence; multifractional process; Gaussian processes;

D O I：

10.1214/07-AIHP127

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：

This paper is devoted to establish an invariance principle where the limit process is a multifractional Gaussian process with a multifractional function which takes its values in (1/2, 1). Some properties, such as regularity and local self-similarity of this process are studied. Moreover the limit process is compared to the multifractional Brownian motion.

引用

页码：475 / 489

页数：15

共 50 条

[1] Invariance principles in Besov spaces, Gaussian processes and long-range dependence
Hajji, S.
Lakhel, E.
[J]. AFRIKA MATEMATIKA, 2013, 24 (03) : 279 - 296
[2] LONG-RANGE INVARIANCE PRINCIPLE REVISITED
CHANDLER, C
GIBSON, AG
[J]. INDIANA UNIVERSITY MATHEMATICS JOURNAL, 1979, 28 (03) : 389 - 403
[3] Option Pricing Under Multifractional Process and Long-Range Dependence
Mattera, Raffaele
Di Sciorio, Fabrizio
[J]. FLUCTUATION AND NOISE LETTERS, 2021, 20 (01):
[4] LONG-RANGE DEPENDENCE PARAMETER ESTIMATION FOR MIXED SPECTRA GAUSSIAN PROCESSES
Arango-Castillo, Lenin
Takahara, Glen
[J]. 2019 IEEE DATA SCIENCE WORKSHOP (DSW), 2019, : 120 - 124
[5] Statistical estimation of nonstationary Gaussian processes with long-range dependence and intermittency
Gao, JT
Anh, V
Heyde, C
[J]. STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2002, 99 (02) : 295 - 321
[6] INVARIANCE PRINCIPLE FOR SCATTERING WITH LONG-RANGE (AND OTHER) POTENTIALS
CHANDLER, C
GIBSON, AG
[J]. INDIANA UNIVERSITY MATHEMATICS JOURNAL, 1976, 25 (05) : 443 - 460
[7] Long-range dependence and rational Gaussian noise
Yang, Yipeng
[J]. STATISTICS, 2024, 58 (02) : 364 - 382
[8] Robust Estimation of the Sample Mean Variance for Gaussian Processes with Long-Range Dependence
Arango-Castillo, Lenin
Takahara, Glen
[J]. 2017 IEEE GLOBAL CONFERENCE ON SIGNAL AND INFORMATION PROCESSING (GLOBALSIP 2017), 2017, : 201 - 205
[9] Non-parametric estimation of the long-range dependence exponent for Gaussian processes
Lang, G
Azaïs, JM
[J]. JOURNAL OF STATISTICAL PLANNING AND INFERENCE, 1999, 80 (1-2) : 59 - 80
[10] Long-range dependence of Markov renewal processes
Vesilo, RA
[J]. AUSTRALIAN & NEW ZEALAND JOURNAL OF STATISTICS, 2004, 46 (01) : 155 - 171

← 1 2 3 4 5 →