Random ergodic theorems and regularizing random weights

Sylvain Durand (1) , Dominique Schneider (1)

1 LAMFA - Laboratoire Amiénois de Mathématique Fondamentale et Appliquée

We study the convergence of pointwise ergodic means for random subsequences, in a universal framework, together with ergodic means which are modulated by random weights. The methods used in this work involve, mainly, Gaussian tools, transference principles and new results on oscillation functions.

Mots clés: 2000 Mathematics Subject Classification: Primary 60G15; 60G42; 60G50; Secondary 28D05 ergodic averages; subsequences; random processes; almost sure convergence; Z d -actions; dynamical systems; spectral lemma; Gaussian random processes

Domaines: Mathématiques [math]

Sylvain Durand, Dominique Schneider. Random ergodic theorems and regularizing random weights. 2003. ⟨hal-03661883⟩