Weak Convergence to Stable L\'evy Processes for Nonuniformly Hyperbolic Dynamical Systems
Dynamical Systems
2015-04-29 v1
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.
Cite
@article{arxiv.1309.6429,
title = {Weak Convergence to Stable L\'evy Processes for Nonuniformly Hyperbolic Dynamical Systems},
author = {Ian Melbourne and Roland Zweimüller},
journal= {arXiv preprint arXiv:1309.6429},
year = {2015}
}
Comments
Accepted for publication in Ann. Inst. H. Poincar\'e (B) Probab. Statist