A pairwise independent stationary stochastic process
type: Item
instance of: scholarly article
title: A pairwise independent stationary stochastic process
zbMATH Open document ID: 0569.60041
DOI: 10.1016/0167-7152(85)90017-3
author: James B. Robertson
author: James M. Womack
published in: Statistics \& Probability Letters
publication date: 1985-01-01T00:00:00Z
review text: Properties of pairwise independent strictly stationary stochastic processes \(X_ n\), \(n\in {\mathbb{Z}}\), with \(P\{X_ n=1\}=P\{X_ n=-1\}=\) are considered. It is shown e.g. that always \(| E(X_ 1X_ 2X_ 3)| \leq\); and there exists one and only one \(X_ n\), \(n\in {\mathbb{Z}}\), having the properties (i) \(X_ n\in \{-1,1\}\), (ii) \(E(X_ n)=0\), (iii) \(X_ n\), \(n\in {\mathbb{Z}}\), is pairwise independent and stationary, (iv) \(\{X_ 1,...,X_{n-1}\}\) and \(X_ n\) are independent for all \(n>1\), (v) \(E(X_ 1X_ 2X_ 3)=\).
Mathematics Subject Classification ID: 60G10
Mathematics Subject Classification ID: 28D05
zbMATH DE Number: 3909445
zbMATH Keywords: ergodic
zbMATH Keywords: weakly mixing
zbMATH Keywords: pairwise independent strictly stationary stochastic processes
MaRDI profile type: Publication
full work available at URL: 0167-7152(85)90017-3
OpenAlex ID: W2060678928
cites work: Q5563135
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cites work: Pairwise independent random variables
cites work: The mixing properties of certain processes related to Markov chains
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description: scientific article; zbMATH DE number 3909445