A Refined Method for Estimating the Global Hölder Exponent

[en] In this paper, we recall basic results we have obtained about generalized Hölder spaces and present a wavelet characterization that holds under more general hypothesis than previously stated. This theoretical tool gives rise to a method for estimating the global Hölder exponent which seems to be more precise than other wavelet-based approaches. This work should prove helpful for estimating long range correlations.

Disciplines :

Mathematics

Author, co-author :

Nicolay, Samuel ; Université de Liège > Département de mathématique > Analyse - Analyse fonctionnelle - Ondelettes

Kreit, Damien

Language :

English

Title :

A Refined Method for Estimating the Global Hölder Exponent

Publication date :

April 2016

Event name :

13th International Conference on Information Technology : New Generations

Event organizer :

Shahram Latifi

Event place :

Las Vegas, United States

Event date :

April 11-13, 2016

Audience :

International

Main work title :

Information Technology: New Generations

Main work alternative title :

[en] 13th International Conference on Information Technology

Editor :

Latifi, Shahram

Publisher :

Springer, Switzerland

Edition :

1st ed.

ISBN/EAN :

978-3-319-32466-1

Collection name :

Advances in Intelligent Systems and Computing 448

Pages :

949-958

Peer reviewed :

Peer reviewed

Available on ORBi :

since 16 April 2016

Statistics

Number of views

81 (16 by ULiège)

Number of downloads

17 (8 by ULiège)

More statistics

Scopus citations^®

Scopus citations^®
without self-citations

OpenCitations

OpenAlex citations

Bibliography

Dahmen, W., Prössdorf, S., Schneider, R.: Wavelet approximation methods for pseudodifferential equations: I Stability and convergence. Math. Z. 215, 583–620 (1994)
Daubechies, I.: Ten Lectures on Wavelets. Society for Industrial and Applied Mathematics (2006)
Jaffard, S.: Wavelet techniques inmultifractal analysis. Proceedings of Symposia in Pure Mathematics 72, 91–152 (2004)
Jaffard, S., Meyer, Y.: Wavelet methods for pointwise regularity and local oscillations of functions. Mem. Am. Math. Soc. 587, 110 (1996)
Khintchine, A.: Über einen Satz derWahrscheinlichkeitsrechnung. Fund. Math. 6, 9–20 (1924)
Kreit, D., Nicolay, S.: Some characterizations of generalized Hölder spaces.Math. Nachr. 285, 2157–2172 (2012)
Kreit, D., Nicolay, S.: Characterizations of the elements of generalized Hölder-Zygmund spaces by means of their representation. J. Approx. Theory 172, 23–36 (2013)
Marquardt, D.: An Algorithm for Least-Squares Estimation of Nonlinear Parameters. J. Soc. Indust. Appl. Math. 11(2), 431–441 (1963)
Meyer, Y.: Ondelettes et opérateurs: Ondelettes, vol. 1. Hermann (1990)
Moura, S.D.: On some characterizations of Besov spaces of generalized smoothness. Math. Nachr. 280(9–10), 1190–1199 (2007)
Samoradnitsky, G., Taqqu, M.S.: Stable Non-Gaussian Random Processes. CRC Press (1994)
Torrence, C., Compo, G.P.: A Practical Guide to Wavelet Analysis. Bull. Amer. Meteor. Soc. 79, 61–78 (1998)