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Series Representations of Fractional Gaussian Processes by Trigonometric and Haar Systems

Dublin Core		PKP Metadata Items	Metadata for this Document
1.	Title	Title of document	Series Representations of Fractional Gaussian Processes by Trigonometric and Haar Systems
2.	Creator	Author's name, affiliation, country	Werner Linde; FSU Jena; Germany
2.	Creator	Author's name, affiliation, country	Antoine Ayache; Université Lille 1; France
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)	Approximation of operators and processes, Rie-mann--Liouville operator, Riemann--Liouville process, Haar system, trigonometric system.
3.	Subject	Subject classification	Primary: 60G15; Secondary: 26A33, 47B06, 41A30
4.	Description	Abstract	The aim of the present paper is to investigate series representations of the Riemann-Liouville process $R^\alpha$, $\alpha >1/2$, generated by classical orthonormal bases in $L_2[0,1]$. Those bases are, for example, the trigonometric or the Haar system. We prove that the representation of $R^\alpha$ via the trigonometric system possesses the optimal convergence rate if and only if $1/2 < \alpha\leq 2$. For the Haar system we have an optimal approximation rate if $1/2 < \alpha <3/2$ while for $\alpha > 3/2$ a representation via the Haar system is not optimal. Estimates for the rate of convergence of the Haar series are given in the cases $\alpha > 3/2$ and $\alpha = 3/2$. However, in this latter case the question whether or not the series representation is optimal remains open. Recently M. A. Lifshits answered this question (cf. [13]). Using a different approach he could show that in the case $\alpha = 3/2$ a representation of the Riemann-Liouville process via the Haar system is also not optimal.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)
7.	Date	(YYYY-MM-DD)	2009-12-21
8.	Type	Status & genre	Peer-reviewed Article
8.	Type	Type
9.	Format	File format	PDF
10.	Identifier	Uniform Resource Identifier	http://ejp.ejpecp.org/article/view/727
10.	Identifier	Digital Object Identifier	10.1214/EJP.v14-727
11.	Source	Journal/conference title; vol., no. (year)	Electronic Journal of Probability; Vol 14
12.	Language	English=en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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