We give optimal convergence rates in the central limit theorem for a large class of martingale difference sequences with bounded third moments. The rates depend on the behaviour of the conditional variances and for stationary sequences the rate $n^{-1/2}\log n$ is reached. We give interesting examples of martingales with unbounded increments which belong to the considered class.
Publié le : 2004-03-23
Classification:
Lindeberg's decomposition,
rate of convergence,
martingale difference sequence,
central limit theorem,
60G42, 60F05,
[MATH.MATH-PR]Mathematics [math]/Probability [math.PR]
@article{hal-00001345,
author = {El Machkouri, Mohamed and Ouchti, Lahcen},
title = {Exact convergence rates in the central limit theorem for a class of martingales},
journal = {HAL},
volume = {2004},
number = {0},
year = {2004},
language = {en},
url = {http://dml.mathdoc.fr/item/hal-00001345}
}
El Machkouri, Mohamed; Ouchti, Lahcen. Exact convergence rates in the central limit theorem for a class of martingales. HAL, Tome 2004 (2004) no. 0, . http://gdmltest.u-ga.fr/item/hal-00001345/