We prove the almost sure invariance principle for a class of abstract dynamical systems including dynamical systems with stretched exponential mixing rates. The result can be applied to chaotic billiards and hyperbolic attractors with Markov sieves as well as expanding maps of the interval and Axiom A diffeomorphisms.
"Almost sure invariance principle for dynamical systems with stretched exponential mixing rates." Hiroshima Math. J. 34 (3) 371 - 411, November 2004. https://doi.org/10.32917/hmj/1150998511