Let $\{X_k\}_{k \in \mathbb{N}}$ be a nonstationary sequence of random variables. Sufficient conditions are found for the existence of an independent sequence $\{\tilde{X}_k\}_{k \in \mathbb{N}}$ such that $\sup_{x \in \mathbb{R}^1}|P(M_n \leq x) - P(\tilde{M}_n \leq x)| \rightarrow 0$ as $n \rightarrow \infty$, where $M_n$ and $\tilde{M}_n$ are $n$th partial maxima for $\{X_k\}$ and $\{\tilde{X}_k\}$, respectively.
Publié le : 1993-04-14
Classification:
Maxima,
phantom distribution function,
asymptotic independent representation,
60G70,
60F99,
60J10
@article{1176989269,
author = {Jakubowski, Adam},
title = {An Asymptotic Independent Representation in Limit Theorems for Maxima of Nonstationary Random Sequences},
journal = {Ann. Probab.},
volume = {21},
number = {4},
year = {1993},
pages = { 819-830},
language = {en},
url = {http://dml.mathdoc.fr/item/1176989269}
}
Jakubowski, Adam. An Asymptotic Independent Representation in Limit Theorems for Maxima of Nonstationary Random Sequences. Ann. Probab., Tome 21 (1993) no. 4, pp. 819-830. http://gdmltest.u-ga.fr/item/1176989269/