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Random series of functions and applications

Frédéric Paccaut·Dominique Schneider
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Abstract

We study the continuity properties of trajectories for some random series of functions $\sum a\_kf(\alpha X\_k(\omega))$ where $a\_k$ is a complex sequence, $X\_k$ a sequence of real independent random variables, $f$ is a real valued function with period one and summable Fourier coefficients. We obtain almost sure continuity results for these periodic or almost periodic series for a large class of functions, where the "almost sure" does not depend on the function.

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Frédéric Paccaut, Dominique Schneider. 2006-02-10. Random series of functions and applications. https://arxiv.org/abs/math/0602207

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