Regularity properties of random wavelet series

Céline Esser, Stéphane Jaffard, Béatrice Vedel

Published 2023-04-03Version 1

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.