It is shown that $\sum^n_{i=1} X_n$ and $\max^n_{i=1}X_i$ are asymptotically independent if $\{X_i\}$ is strongly mixing and $\sum^n_{i=1} X_i$ is asymptotically Gaussian. This generalizes a result of Anderson and Turkman.
Publié le : 1995-04-14
Classification:
Central limit theorem,
extreme values,
strong mixing,
60F05
@article{1176988296,
author = {Hsing, Tailen},
title = {A Note on the Asymptotic Independence of the Sum and Maximum of Strongly Mixing Stationary Random Variables},
journal = {Ann. Probab.},
volume = {23},
number = {3},
year = {1995},
pages = { 938-947},
language = {en},
url = {http://dml.mathdoc.fr/item/1176988296}
}
Hsing, Tailen. A Note on the Asymptotic Independence of the Sum and Maximum of Strongly Mixing Stationary Random Variables. Ann. Probab., Tome 23 (1995) no. 3, pp. 938-947. http://gdmltest.u-ga.fr/item/1176988296/