Exponential inequalities for dynamical measures of expanding maps of the interval
成果类型：
Article
署名作者：
Collet, P; Martinez, S; Schmitt, B
署名单位：
Institut Polytechnique de Paris; Ecole Polytechnique; Centre National de la Recherche Scientifique (CNRS); CNRS - Institute of Physics (INP); Universidad de Chile; Universidad de Chile; Universite Bourgogne Europe
刊物名称：
PROBABILITY THEORY AND RELATED FIELDS
ISSN/ISSBN：
0178-8051
DOI：
10.1007/s004400200204
发表日期：
2002
页码：
301-322
关键词：
摘要：
We prove an exponential inequality for the absolutely continuous invariant measure of a piecewise expanding map of the interval. As an immediate corollary we obtain a concentration inequality. We apply these results to the estimation of the rate of convergence of the empirical measure in various metrics and also to the efficiency of the shadowing by sets of positive measure.