The Annals of Applied Probability

On lacunary wavelet series

Stéphane Jaffard

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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.

Article information

Source
Ann. Appl. Probab., Volume 10, Number 1 (2000), 313-329.

Dates
First available in Project Euclid: 25 April 2002

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1019737675

Digital Object Identifier
doi:10.1214/aoap/1019737675

Mathematical Reviews number (MathSciNet)
MR1765214

Zentralblatt MATH identifier
1063.60053

Subjects
Primary: 60G17: Sample path properties
Secondary: 26A15: Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) {For properties determined by Fourier coefficients, see 42A16; for those determined by approximation properties, see 41A25, 41A27} 28A80: Fractals [See also 37Fxx]

Keywords
Wavelet bases Hausdorff dimensions chirps Hölder regularity modulus of continuity

Citation

Jaffard, Stéphane. On lacunary wavelet series. Ann. Appl. Probab. 10 (2000), no. 1, 313--329. doi:10.1214/aoap/1019737675. https://projecteuclid.org/euclid.aoap/1019737675


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