Almost Sure Central Limit Theorems and the Erdos-Renyi law for Expanding Maps of the Interval
| dc.creator | Chazottes, J. -R. | |
| dc.creator | Collet, P. | |
| dc.date | 2002-10-18 | |
| dc.date | 2008-05-15 | |
| dc.date.accessioned | 2026-07-07T09:38:53Z | |
| dc.date.available | 2026-07-07T09:38:53Z | |
| dc.description | For a large class of expanding maps of the interval, we prove that partial sums of Lipschitz observables satisfy an almost sure central limit theorem (ASCLT). In fact, we provide a speed of convergence in the Kantorovich metric. Maxima of partial sums are also shown to obey an ASCLT. The key-tool is an exponential inequality recently obtained. Then we derive almost-sure convergence rates for the supremum of moving averages of Lipschitz observables (Erdos-Renyi type law). We end up with an application to entropy estimation ASCLT's that refi ne Shannon-McMillan-Breiman and Ornstein-Weiss theorems. | |
| dc.description | 25p; title has changed; minor corrections; published in Erg. Th. Dynam. Sys. (2005) | |
| dc.identifier | https://arxiv.org/abs/math/0210286 | |
| dc.identifier | http://arxiv.org/abs/math/0210286 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/160976 | |
| dc.subject | Probability | |
| dc.subject | Dynamical Systems | |
| dc.title | Almost Sure Central Limit Theorems and the Erdos-Renyi law for Expanding Maps of the Interval | |
| dc.type | text |