Weak Convergence to Stable Lévy Processes for Nonuniformly Hyperbolic Dynamical Systems.

Ann. Inst. H. Poincaré Probab. Statist. 51 (2015) 545-556.

Ian Melbourne and Roland Zweimüller.

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 the M₁ topology.