On lacunary wavelet series

被引：61
|
作者：
Jaffard, S [1 ]
机构：
[1] Univ Paris 12, Fac Sci & Technol, Dept Math, F-94010 Creteil, France
来源：
ANNALS OF APPLIED PROBABILITY | 2000年 / 10卷 / 01期
关键词：
wavelet bases; Hausdorff dimensions; chirps; Holder regularity; modulus of continuity;
D O I：
10.1214/aoap/1019737675
中图分类号：
O21 [概率论与数理统计]; C8 [统计学];
学科分类号：
020208 ; 070103 ; 0714 ;
摘要：
We prove that the Holder 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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页码：313 / 329
页数：17
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