On random almost periodic series and random ergodic theory

摘要

In this paper we obtain different types of random ergodic theorems for dynamical systems or continuous semi-flows. These results recover and extend previous works on dynamical systems and are completely new in the case of semi-flows. The proofs are based on uniform estimates on random almost periodic polynomials that we obtained very recently and on an improvement of a tool introduced by Talagrand in 1995 and further developed by Fernique in 1996. In the course of this, we partially recover results of Marcus and Pisier from the 1980s on almost sure uniform convergence of random almost periodic series.