This paper contains necessary and sufficient conditions, which sometimes coincide, for the limiting distribution of a uniformly (or strongly) mixing stationary process to be the same as for the independent process with the same marginal distributions. Examples with different limits are given. Let $H$ be any distribution function and let $c_n(\xi) = \inf \{x \in R: H(x) \geqq 1 - \xi/n\}$. The limiting behavior of $H^n(c_n(\xi))$ is determined.
Publié le : 1974-06-14
Classification:
Limit distributions,
maximum value,
stationary process,
uniform or strong mixing,
independent process,
60F05,
60G10
@article{1176996673,
author = {O'Brien, G. L.},
title = {Limit Theorems for the Maximum Term of a Stationary Process},
journal = {Ann. Probab.},
volume = {2},
number = {6},
year = {1974},
pages = { 540-545},
language = {en},
url = {http://dml.mathdoc.fr/item/1176996673}
}
O'Brien, G. L. Limit Theorems for the Maximum Term of a Stationary Process. Ann. Probab., Tome 2 (1974) no. 6, pp. 540-545. http://gdmltest.u-ga.fr/item/1176996673/