The Billard Theorem for Multiple Random Fourier Series

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• 作者：Samuel Ronsin ; Hermine Biermé…
• 关键词：Billard Theorem ; Random Fourier series ; Multiple Fourier series ; Random phase ; Random fields
• 刊名：Journal of Fourier Analysis and Applications
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：23
• 期：1
• 页码：207-228
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Fourier Analysis; Signal,Image and Speech Processing; Abstract Harmonic Analysis; Approximations and Expansions; Partial Differential Equations; Mathematical Methods in Physics;
• 出版者：Springer US
• ISSN：1531-5851
• 卷排序：23

文摘

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.