## The Annals of Probability

### An Asymptotic Independent Representation in Limit Theorems for Maxima of Nonstationary Random Sequences

#### Abstract

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.

#### Article information

Source
Ann. Probab., Volume 21, Number 2 (1993), 819-830.

Dates
First available in Project Euclid: 19 April 2007

https://projecteuclid.org/euclid.aop/1176989269

Digital Object Identifier
doi:10.1214/aop/1176989269

Mathematical Reviews number (MathSciNet)
MR1217567

Zentralblatt MATH identifier
0781.60042

JSTOR