Almost sure invariance principle for sequential and non-stationary dynamical systems

International audienceWe establish almost sure invariance principles, a strong form of approximationby Brownian motion, for non-stationary time-series arising as observationson dynamical systems. Our examples include observations on sequentialexpanding maps, perturbed dynamical systems, non-stationary sequences offunctions on hyperbolic systems as well as applications to the shrinking targetproblem in expanding systems