A central limit theorem is proved for some strictly stationary $\rho$-mixing sequences with infinite second moments. The condition on the tails of the marginal distribution is the same as in the corresponding classic result for i.i.d. sequences. The mixing rate is essentially the slowest possible for this result.
Publié le : 1988-01-14
Classification:
Strictly stationary,
$\rho$-mixing,
infinite variance,
central limit theorem,
60F05,
60G10
@article{1176991904,
author = {Bradley, Richard C.},
title = {A Central Limit Theorem for Stationary $\rho$-Mixing Sequences with Infinite Variance},
journal = {Ann. Probab.},
volume = {16},
number = {4},
year = {1988},
pages = { 313-332},
language = {en},
url = {http://dml.mathdoc.fr/item/1176991904}
}
Bradley, Richard C. A Central Limit Theorem for Stationary $\rho$-Mixing Sequences with Infinite Variance. Ann. Probab., Tome 16 (1988) no. 4, pp. 313-332. http://gdmltest.u-ga.fr/item/1176991904/