TY - JOUR
T1 - A concentration inequality for interval maps with an indifferent fixed point
AU - Chazottes, J.-R.
AU - Collet, P.
AU - Redig, F.
AU - Verbitskiy, E.
N1 - Relation: http://www.rug.nl/informatica/organisatie/overorganisatie/iwi
Rights: University of Groningen, Research Institute for Mathematics and Computing Science (IWI)
PY - 2009/8
Y1 - 2009/8
N2 - For a map of the unit interval with an indifferent fixed point, we prove an upper bound for the variance of all observables of n variables, K : [0, 1]^n → R, which are separately Lipschitz. The proof is based on coupling and decay of correlation properties of the map. We also present applications of this inequality to the almost-sure central limit theorem, the kernel density estimation, the empirical measure and the periodogram.
AB - For a map of the unit interval with an indifferent fixed point, we prove an upper bound for the variance of all observables of n variables, K : [0, 1]^n → R, which are separately Lipschitz. The proof is based on coupling and decay of correlation properties of the map. We also present applications of this inequality to the almost-sure central limit theorem, the kernel density estimation, the empirical measure and the periodogram.
U2 - 10.1017/S0143385708000588
DO - 10.1017/S0143385708000588
M3 - Article
SN - 0143-3857
VL - 29
SP - 1097
EP - 1117
JO - Ergodic Theory and Dynamical Systems
JF - Ergodic Theory and Dynamical Systems
IS - 4
ER -