We prove a central limit theorem for strongly mixing sequences under
a sharp sufficient condition which combines the rate of the strong mixing
coefficient with the quantile function. The result improves on all earlier
central limit theorems for this type of dependence and answers a conjecture
raised by Bradley in 1997.
¶ Moreover, we derive the corresponding functional central limit
theorem.
Publié le : 2000-06-14
Classification:
Strong mixing,
central limit theorem,
weak invariance principle,
quantiles,
60F05,
60F17
@article{1019160337,
author = {Merlev\`ade, Florence and Peligrad, Magda},
title = {The functional central limit theorem under the strong mixing
condition},
journal = {Ann. Probab.},
volume = {28},
number = {1},
year = {2000},
pages = { 1336-1352},
language = {en},
url = {http://dml.mathdoc.fr/item/1019160337}
}
Merlevàde, Florence; Peligrad, Magda. The functional central limit theorem under the strong mixing
condition. Ann. Probab., Tome 28 (2000) no. 1, pp. 1336-1352. http://gdmltest.u-ga.fr/item/1019160337/