Regularity properties of random wavelet series

[en] 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.

Disciplines :

Mathematics

Author, co-author :

Esser, Céline ; Université de Liège - ULiège > Mathematics

Jaffard, Stéphane ; Université de Liège - ULiège > Département de mathématique > Analyse - Analyse fonctionnelle - Ondelettes

Vedel, Béatrice

Language :

English

Title :

Regularity properties of random wavelet series

Publication date :

2024

Journal title :

Theory of Probability and Mathematical Statistics

ISSN :

0094-9000

eISSN :

1547-7363

Publisher :

American Mathematical Society, Providence, United States - Rhode Island

Volume :

110

Pages :

31-53

Peer reviewed :

Peer Reviewed verified by ORBi

Commentary :

26 pages

Available on ORBi :

since 14 April 2023

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