Article contents
A concentration inequality for interval maps with an indifferent fixed point
Published online by Cambridge University Press: 01 August 2009
Abstract
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.
- Type
- Research Article
- Information
- Copyright
- Copyright © Cambridge University Press 2009
References
- 4
- Cited by