Random series of functions and applications

Frédéric Paccaut (1) , Dominique Schneider (2)

1 LAMFA - Laboratoire Amiénois de Mathématique Fondamentale et Appliquée
2 LMPA - Laboratoire de Mathématiques Pures et Appliquées Joseph Liouville

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.

Mots clés: random fourier series; gaussian randomization; almost periodic functions; random trigonometric polynomial; random fourier series

Domaines: Probabilités [math.PR]

Frédéric Paccaut, Dominique Schneider. Random series of functions and applications. 2006. ⟨hal-00018814⟩