Wavelet-type expansion of generalized ...
Document type :
Article dans une revue scientifique: Article original
Permalink :
Title :
Wavelet-type expansion of generalized Rosenblatt process and its rate of convergence
Author(s) :
Ayache, Antoine [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Esmili, Yassine [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Esmili, Yassine [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Journal title :
Journal of Fourier Analysis and Applications
Publisher :
Springer Verlag
Publication date :
2020
ISSN :
1069-5869
English keyword(s) :
Wiener chaos
self-similar processes
multiresolution analyses
wavelet bases
random series
self-similar processes
multiresolution analyses
wavelet bases
random series
HAL domain(s) :
Mathématiques [math]
Mathématiques [math]/Probabilités [math.PR]
Mathématiques [math]/Probabilités [math.PR]
English abstract : [en]
Pipiras introduced in the early 2000s an almost surely and uniformly convergent (on compact intervals) wavelet-type expansion of classical Rosenblatt process. Yet, the issue of estimating, almost surely, its uniform rate ...
Show more >Pipiras introduced in the early 2000s an almost surely and uniformly convergent (on compact intervals) wavelet-type expansion of classical Rosenblatt process. Yet, the issue of estimating, almost surely, its uniform rate of convergence remained an open question. The main goal of our present article is to provide an answer to it in the more general framework of generalized Rosenblatt process, under the assumption that the underlying wavelet basis belongs to the class due to Meyer. The main ingredient of our strategy consists in expressing in a non-classical (new) way the approximation errors related with the approximation spaces of a multiresolution analysis of L 2 (R 2). Such a non-classical expression may also be of interest in its own right.Show less >
Show more >Pipiras introduced in the early 2000s an almost surely and uniformly convergent (on compact intervals) wavelet-type expansion of classical Rosenblatt process. Yet, the issue of estimating, almost surely, its uniform rate of convergence remained an open question. The main goal of our present article is to provide an answer to it in the more general framework of generalized Rosenblatt process, under the assumption that the underlying wavelet basis belongs to the class due to Meyer. The main ingredient of our strategy consists in expressing in a non-classical (new) way the approximation errors related with the approximation spaces of a multiresolution analysis of L 2 (R 2). Such a non-classical expression may also be of interest in its own right.Show less >
Language :
Anglais
Peer reviewed article :
Oui
Audience :
Internationale
Popular science :
Non
Collections :
Source :
Submission date :
2025-01-24T17:07:14Z
Files
- document
- Open access
- Access the document
- WavRos1.pdf
- Open access
- Access the document