Exchangeable random variables and the subsequence principle
type: Item
instance of: scholarly article
title: Exchangeable random variables and the subsequence principle
zbMATH Open document ID: 0572.60027
DOI: 10.1007/BF00776240
author: István Berkes
author: E. Péter
publication date: 1986-01-01T00:00:00Z
review text: Call a sequence \(\{X_ n\}\) of r.v.'s \(\epsilon\)-exchangeable if on the same probability space there exists an exchangeable sequence \(\{Y_ n\}\) such that \(P(| X_ n-Y_ n| \geq \epsilon)\leq \epsilon\) for all n. We prove that any tight sequence \(\{X_ n\}\) defined on a rich enough probability space contains \(\epsilon\)-exchangeable subsequences for every \(\epsilon >0\). The distribution of the approximating exchangeable sequences is also described in terms of \(\{X_ n\}\). Our results give a convenient way to prove limit theorems for subsequences of general r.v. sequences. In particular, they provide a simplified way to prove the subsequence theorems of \textit{D. J. Aldous} [Z. Wahrscheinlichkeitstheor. Verw. Geb. 40, 59-82 (1977)] and lead also to various extensions.
Mathematics Subject Classification ID: 60F05
Mathematics Subject Classification ID: 60G09
zbMATH DE Number: 3913351
zbMATH Keywords: exchangeable sequence
zbMATH Keywords: tight sequence
zbMATH Keywords: \(\epsilon \) -exchangeable subsequences
zbMATH Keywords: limit theorems for subsequences
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf00776240
OpenAlex ID: W2030171005
published in: Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
description: scientific article; zbMATH DE number 3913351