Davydov showed that in a classic central limit theorem of Ibragimov under the strong mixing condition, the combinations of mixing rate and moment assumption were practically as weak as permissible. Here some constructions will be given to show that Davydov's observation still holds under the additional assumption that the growth of $\operatorname{var}(X_1 + \cdots + X_n)$ be asymptotically linear. Our constructions will be similar to a recent one of Herrndorf.
Publié le : 1985-11-14
Classification:
Strong mixing,
absolute regularity,
central limit theorem,
60G10,
60F05
@article{1176992815,
author = {Bradley, Richard C.},
title = {On the Central Limit Question Under Absolute Regularity},
journal = {Ann. Probab.},
volume = {13},
number = {4},
year = {1985},
pages = { 1314-1325},
language = {en},
url = {http://dml.mathdoc.fr/item/1176992815}
}
Bradley, Richard C. On the Central Limit Question Under Absolute Regularity. Ann. Probab., Tome 13 (1985) no. 4, pp. 1314-1325. http://gdmltest.u-ga.fr/item/1176992815/