Abstract
In this paper, we propose a class of stochastic processes having an extended self-similarity property as well as intermittency. These notions are characterized with two parameters, and we propose statistical estimators for them.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
B. Mandelbrot Fractal Geometry of Nature. W.H. Freeman and Company, New York, 1983.
Lévy Véhel, Lutton, and Tricot, editors Fractals in Engineerin g. Springer-Verlag, berlin and New York, 1997.
A. Benassi, S. Jaffard, and D. Roux, Gaussian processes and pseudo-differential elliptic operators. Revista Mathematica Iberoamericana 13 (1):19–89, 1997.
U. Frisch Turbulence. Cambridge University Press, Cambridge, England, 1995.
J. Lévy Véhel, Texture analysis using fractal probability functions. INRIA 1992.
A. R. Rao A Taxonomy for Texture Description and Identification. Springer-Verlag, Berlin and New York, 1999.
A. M. Jaglom, Some classes of random fields in n-dimensional space related to stationary random processes. Theor. Probability Appl. 2:292–337, 1957.
R. L. Dobrushin, Gaussian and their subordinated self similar random fields. Ann. Proba. 7:1–28, 1979.
G. Bourdaud, Réalisation des espaces de Besov homogènes. Arkin Math. 26:41–54, 1988.
Y. Meyer Ondelettes et Algorithmes Concurents. Hermann ed, Paris, 1992.
A. Benassi, S. Cohen, J. Istas, and S. Jaffard, Identification of filtered white noises. Stoch. Processes and their Applications 75:31–49, 1998.
R. Lyons, Random walk and percolation on tree. Ann. Proba. 18 (3):937–958, 1990.
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2003 Springer Science+Business Media New York
About this chapter
Cite this chapter
Benassi, A., Cohen, S., Deguy, S., Istas, J. (2003). Self-Similarity and Intermittency. In: Debnath, L. (eds) Wavelets and Signal Processing. Applied and Numerical Harmonic Analysis. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0025-3_11
Download citation
DOI: https://doi.org/10.1007/978-1-4612-0025-3_11
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-1-4612-6578-8
Online ISBN: 978-1-4612-0025-3
eBook Packages: Springer Book Archive