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
收藏
页码：1198 / 1221
页数：24
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