The Billard Theorem for Multiple Random Fourier Series
نویسندگان
چکیده
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. AMS 2010 Mathematics Subject Classification. Primary: 42B05, 60G60, 60G17; Secondary: 42B08, 60G50. keywords: Billard Theorem; Random Fourier series; Multiple Fourier series; Random phase; Random fields.
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