Almost sure invariance principle for sequential and non-stationary   dynamical systems
  We establish almost sure invariance principles, a strong form of approximation by Brownian motion, for non-stationary time-series arising as observations on dynamical systems. Our examples include observations on sequential expanding maps, perturbed dynamical systems, non-stationary sequences of functions on hyperbolic systems as well as applications to the shrinking target problem in expanding systems. 
N. Haydn, M. Nicol, A. T\^or\^ok, S. Vaienti
math.DS