For a class of expansive transformations of the unit interval, we show a local limit theorem for the process $(f \circ T^n)_{n \in N}$, where $f$ is a real bounded variation function. We show also, that the speed in the central limit theorem is $1/\sqrt n$.
Publié le : 1983-08-14
Classification:
Central limit theorem,
local limit theorem,
60F05,
60J05,
60J10,
10K05,
28D05
@article{1176993522,
author = {Rousseau-Egele, J.},
title = {Un Theoreme de la Limite Locale Pour une Classe de Transformations Dilatantes et Monotones par Morceaux},
journal = {Ann. Probab.},
volume = {11},
number = {4},
year = {1983},
pages = { 772-788},
language = {fr},
url = {http://dml.mathdoc.fr/item/1176993522}
}
Rousseau-Egele, J. Un Theoreme de la Limite Locale Pour une Classe de Transformations Dilatantes et Monotones par Morceaux. Ann. Probab., Tome 11 (1983) no. 4, pp. 772-788. http://gdmltest.u-ga.fr/item/1176993522/