The Annals of Probability

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

Adam Jakubowski

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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

Permanent link to this document
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
links.jstor.org

Subjects
Primary: 60G70: Extreme value theory; extremal processes
Secondary: 60F99: None of the above, but in this section 60J10: Markov chains (discrete-time Markov processes on discrete state spaces)

Keywords
Maxima phantom distribution function asymptotic independent representation

Citation

Jakubowski, Adam. An Asymptotic Independent Representation in Limit Theorems for Maxima of Nonstationary Random Sequences. Ann. Probab. 21 (1993), no. 2, 819--830. doi:10.1214/aop/1176989269. https://projecteuclid.org/euclid.aop/1176989269


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