We show that Billard's theorem on a.s. uniform convergence of random Fourier series with independent symmetric coefficients is not true when the coefficients are only assumed to be centered independent. We give some necessary or sufficient conditions to ensure the validity of Billard's theorem in the centered case.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ba53-1-5,
author = {Guy Cohen and Christophe Cuny},
title = {On Billard's Theorem for Random Fourier Series},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
volume = {53},
year = {2005},
pages = {39-53},
zbl = {1112.42002},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba53-1-5}
}
Guy Cohen; Christophe Cuny. On Billard's Theorem for Random Fourier Series. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 53 (2005) pp. 39-53. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba53-1-5/