Expansions For Gaussian Processes And Parseval Frames

被引：14

作者：

Luschgy, Harald ^{[1
]}

Pages, Gilles ^{[2
]}

机构：

[1] Univ Trier, FB Math 4, D-54286 Trier, Germany

[2] Univ Paris 06, Lab Probabil & Modeles Aleatoires, UMR 7599, F-75252 Paris 5, France

来源：

ELECTRONIC JOURNAL OF PROBABILITY | 2009年 / 14卷

关键词：

Gaussian process; series expansion; Parseval frame; optimal expansion; fractional Ornstein-Uhlenbeck process; FRACTIONAL BROWNIAN-MOTION; SERIES EXPANSION; QUANTIZATION; ASYMPTOTICS; OPTIMALITY;

D O I：

10.1214/EJP.v14-649

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：

We derive a precise link between series expansions of Gaussian random vectors in a Banach space and Parseval frames in their reproducing kernel Hilbert space. The results are applied to pathwise continuous Gaussian processes and a new optimal expansion for fractional Ornstein-Uhlenbeck processes is derived.

引用

页码：1198 / 1221

页数：24

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