Devroye Inequality for a Class of Non-Uniformly Hyperbolic Dynamical Systems
Abstract
In this paper, we prove an inequality, which we call "Devroye inequality", for a large class of non-uniformly hyperbolic dynamical systems (M,f). This class, introduced by L.-S. Young, includes families of piece-wise hyperbolic maps (Lozi-like maps), scattering billiards (e.g., planar Lorentz gas), unimodal and H{\'e}non-like maps. Devroye inequality provides an upper bound for the variance of observables of the form K(x,f(x),...,f^{n-1}(x)), where K is any separately Holder continuous function of n variables. In particular, we can deal with observables which are not Birkhoff averages. We will show in \cite{CCS} some applications of Devroye inequality to statistical properties of this class of dynamical systems.
Cite
@article{arxiv.math/0412166,
title = {Devroye Inequality for a Class of Non-Uniformly Hyperbolic Dynamical Systems},
author = {J. -R. Chazottes and P. Collet and B. Schmitt},
journal= {arXiv preprint arXiv:math/0412166},
year = {2009}
}
Comments
Corrected version; To appear in Nonlinearity