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

VL - 29

SP - 1097

EP - 1117

JO - Ergodic Theory and Dynamical Systems

JF - Ergodic Theory and Dynamical Systems

SN - 0143-3857

IS - 4

ER -