On Billard's Theorem for Random Fourier Series
Volume 53 / 2005
Bulletin Polish Acad. Sci. Math. 53 (2005), 39-53
MSC: Primary 42A61, 60G17; Secondary 60G50.
DOI: 10.4064/ba53-1-5
Abstract
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.
