Weak Convergence to Stable L\'evy Processes for Nonuniformly Hyperbolic Dynamical Systems

Understand

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.