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April, 1995 A Borderline Random Fourier Series
Michel Talagrand
Ann. Probab. 23(2): 776-785 (April, 1995). DOI: 10.1214/aop/1176988289


Consider a mean zero random variable $X$, and an independent sequence $(X_n)$ distributed like $X$. We show that the random Fourier series $\sum_{n\geq 1} n^{-1} X_n \exp(2i\pi nt)$ converges uniformly almost surely if and only if $E(|X|\log\log(\max(e^e, |X|))) < \infty$.


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Michel Talagrand. "A Borderline Random Fourier Series." Ann. Probab. 23 (2) 776 - 785, April, 1995.


Published: April, 1995
First available in Project Euclid: 19 April 2007

zbMATH: 0830.60035
MathSciNet: MR1334171
Digital Object Identifier: 10.1214/aop/1176988289

Primary: 42A61
Secondary: 60G17 , 60G50

Keywords: integrability condition , Uniform convergence

Rights: Copyright © 1995 Institute of Mathematical Statistics

Vol.23 • No. 2 • April, 1995
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