Vector-valued almost sure invariance principles for (non)stationary and random dynamical systems

Abstract

We study the limit behavior of (non)stationary and random chaotic dynamical systems. Several (vector-valued) almost sure invariance principles for (non)stationary dynamical systems and quenched (vector-valued) almost sure invariance principles for random dynamical systems are proved. We also apply our results to stationary chaotic dynamical systems, which admit Young towers, and to (non)uniformly expanding non-stationary and random dynamical systems with intermittencies or uniform spectral gaps. It implies that the systems under study tend to a Brownian motion under various scalings.