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February 2000 On lacunary wavelet series
Stéphane Jaffard
Ann. Appl. Probab. 10(1): 313-329 (February 2000). DOI: 10.1214/aoap/1019737675

Abstract

We prove that the Hölder singularities of random lacunary wavelet series are chirps located on random fractal sets. We determine the Hausdorff dimensions of these singularities, and the a.e. modulus of continuity of the series. Lacunary wavelet series thus turn out to be a new example of multifractal functions.

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Stéphane Jaffard. "On lacunary wavelet series." Ann. Appl. Probab. 10 (1) 313 - 329, February 2000. https://doi.org/10.1214/aoap/1019737675

Information

Published: February 2000
First available in Project Euclid: 25 April 2002

zbMATH: 1063.60053
MathSciNet: MR1765214
Digital Object Identifier: 10.1214/aoap/1019737675

Subjects:
Primary: 60G17
Secondary: 26A15, 28A80

Rights: Copyright © 2000 Institute of Mathematical Statistics

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Vol.10 • No. 1 • February 2000
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