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The Billard Theorem for Multiple Random Fourier Series

Abstract : We propose a generalization of a classical result on random Fourier series, namely the Billard Theorem, for random Fourier series over the d-dimensional torus. We provide an investigation of the independence with respect to a choice of a sequence of partial sums (or method of summation). We also study some probabilistic properties of the resulting sum field such as stationarity and characteristics of the marginal distribution.
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Contributor : Lionel Moisan <>
Submitted on : Monday, October 24, 2016 - 4:08:28 PM
Last modification on : Friday, April 10, 2020 - 5:26:52 PM


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Samuel Ronsin, Hermine Biermé, Lionel Moisan. The Billard Theorem for Multiple Random Fourier Series. Journal of Fourier Analysis and Applications, Springer Verlag, 2017, 23 (1), pp.207-228. ⟨10.1007/s00041-016-9467-9⟩. ⟨hal-00850112v2⟩