Weak Convergence to Stable Lévy Processes for Nonuniformly Hyperbolic Dynamical Systems

Abstract

We consider weak invariance principles (functional limit theorems) in the domain of a stable law. A general result is obtained on lifting such limit laws from an induced dynamical system to the original system. An important class of examples covered by our result are Pomeau-Manneville intermittency maps, where convergence for the induced system is in the standard Skorohod J1 topology. For the full system, convergence in the J1 topology fails, but we prove convergence in theM1 topology.