We obtain a nonuniform estimate of the rate of convergence in the martingale central limit theorem for convergence to mixtures of normal distributions. The uniform rates of convergence obtained by several other authors are special cases of our nonuniform estimate. We also obtain a rate of convergence in B. M. Brown's central limit theorem, assuming only Brown's elementary conditions. This result is a martingale analogue of Feller's generalization of the Berry-Esseen theorem.
Publié le : 1981-06-14
Classification:
G0F05,
Martingale central limit theorem,
mixtures of normal distributions,
nonuniform bound,
rate of convergence,
uniform bound,
60G42
@article{1176994413,
author = {Hall, Peter and Heyde, C. C.},
title = {Rates of Convergence in the Martingale Central Limit Theorem},
journal = {Ann. Probab.},
volume = {9},
number = {6},
year = {1981},
pages = { 395-404},
language = {en},
url = {http://dml.mathdoc.fr/item/1176994413}
}
Hall, Peter; Heyde, C. C. Rates of Convergence in the Martingale Central Limit Theorem. Ann. Probab., Tome 9 (1981) no. 6, pp. 395-404. http://gdmltest.u-ga.fr/item/1176994413/