A Vector-Valued Almost Sure Invariance Principle for Hyperbolic Dynamical Systems
Dynamical Systems
2014-12-09 v1 Probability
Abstract
We prove an almost sure invariance principle (approximation by d-dimensional Brownian motion) for vector-valued Holder observables of large classes of nonuniformly hyperbolic dynamical systems. These systems include Axiom~A diffeomorphisms and flows as well as systems modelled by Young towers with moderate tail decay rates. In particular, the position variable of the planar periodic Lorentz gas with finite horizon approximates a 2-dimensional Brownian motion.
Cite
@article{arxiv.math/0606535,
title = {A Vector-Valued Almost Sure Invariance Principle for Hyperbolic Dynamical Systems},
author = {Ian Melbourne and Matthew Nicol},
journal= {arXiv preprint arXiv:math/0606535},
year = {2014}
}