In this talk we will consider limit theorems associated to power variation functionals of some stationary stochastic processes with long range dependence. Due to the long range dependence we cannot use the classical results for Markov chains, martingale differences or different mixing conditions which relies on short memory. Our main focus will be on a class of stable self-similar processes (“random fractals”), that is, where the processes are invariant in distribution under suitable scaling of time and space.