REGULARITY PROPERTIES OF RANDOM WAVELET SERIES

被引：0
|
作者：
Esser, Celine [1 ]
Jaffard, Stephane [2 ]
Vedel, Beatrice [3 ]
机构：
[1] Univ Liege, Bat B37 Zone Polytech,Allee Decouverte 12, B-4000 Liege, Belgium
[2] Univ Gustave Eiffel, Univ Paris Est Creteil, CNRS, LAMA,UMR8050, F-94010 Creteil, France
[3] Univ Bretagne Sud, CNRS, LMBA, UMR 6205, F-56000 Vannes, France
来源：
THEORY OF PROBABILITY AND MATHEMATICAL STATISTICS | 2024年 / 110卷
关键词：
Random wavelet series; random Fourier series; unconditional bases; generic regularity; FOURIER-SERIES;
D O I：
10.1090/tpms/1205
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 study the regularity properties of random wavelet series constructed by multiplying the coefficients of a deterministic wavelet series with unbounded I.I.D. random variables. In particular, we show that, at the opposite to what happens for Fourier series, the randomization of almost every continuous function gives an almost surely nowhere locally bounded function.
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页码：31 / 53
页数：23
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