On the central and local limit theorem for martingale difference sequences
| dc.creator | Machkouri, Mohamed El | |
| dc.creator | Volny, Dalibor | |
| dc.date | 2004-02-28 | |
| dc.date.accessioned | 2026-07-07T05:05:48Z | |
| dc.date.available | 2026-07-07T05:05:48Z | |
| dc.description | Let $(Ω, \A, μ)$ be a Lebesgue space and $T$ an ergodic measure preserving automorphism on $Ω$ with positive entropy. We show that there is a bounded and strictly stationary martingale difference sequence defined on $Ω$ with a common non-degenerate lattice distribution satisfying the central limit theorem with an arbitrarily slow rate of convergence and not satisfying the local limit theorem. A similar result is established for martingale difference sequences with densities provided the entropy is infinite. In addition, the martingale difference sequence may be chosen to be strongly mixing. | |
| dc.description | Accepte pour publication dans Stochastics and Dynamics | |
| dc.identifier | https://arxiv.org/abs/math/0403008 | |
| dc.identifier | http://arxiv.org/abs/math/0403008 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/70305 | |
| dc.subject | Probability | |
| dc.subject | 60F99, 28D05 | |
| dc.title | On the central and local limit theorem for martingale difference sequences | |
| dc.type | text |