A concentration inequality for interval maps with an indifferent fixed pointChazottes, J-R., Collet, P., Redig, F. & Verbitskiy, E., Aug-2009, In : Ergodic Theory and Dynamical Systems. 29, 4, p. 1097-1117 21 p.
Research output: Contribution to journal › Article › Academic
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.
|Number of pages||21|
|Journal||Ergodic Theory and Dynamical Systems|
|Publication status||Published - Aug-2009|