A Borderline Random Fourier Series
Talagrand, Michel
Ann. Probab., Tome 23 (1995) no. 3, p. 776-785 / Harvested from Project Euclid
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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 $E(|X|\log\log(\max(e^e, |X|))) < \infty$.
Publié le : 1995-04-14
Classification:  Uniform convergence,  integrability condition,  42A61,  60G17,  60G50 
@article{1176988289,
     author = {Talagrand, Michel},
     title = {A Borderline Random Fourier Series},
     journal = {Ann. Probab.},
     volume = {23},
     number = {3},
     year = {1995},
     pages = { 776-785},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176988289}
}

Talagrand, Michel. A Borderline Random Fourier Series. Ann. Probab., Tome 23 (1995) no. 3, pp.  776-785. http://gdmltest.u-ga.fr/item/1176988289/