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

Accepted for publication in Ann. Inst. H. Poincaré (B) Probab. Statist

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