On Billard's Theorem for Random Fourier Series

Volume 53 / 2005

Guy Cohen, Christophe Cuny Bulletin Polish Acad. Sci. Math. 53 (2005), 39-53 MSC: Primary 42A61, 60G17; Secondary 60G50. DOI: 10.4064/ba53-1-5


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.


  • Guy CohenDepartment of Mathematics
    Ben Gurion University
    P.O.B. 653
    841105 Beer Sheva, Israel
    Erwin Schrödinger Institute
    Boltzmanngasse 9
    A-1090 Wien, Austria
  • Christophe CunyDepartment of Mathematics
    University of New Caledonia
    Equipe ERIM
    B.P. 4477
    F-98847 Noumea Cedex, France

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