Weak Convergence to Stable Lévy Processes for Nonuniformly Hyperbolic Dynamical Systems

Ian Melbourne, Roland Zweimüller

Published 2013-09-25Version 1

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 J_1 topology. For the full system, convergence in the J_1 topology fails, but we prove convergence in the M_1 topology.