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A pairwise independent stationary stochastic process. (English) Zbl 0569.60041
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) \(E(X_ 1X_ 2X_ 3)=\).
Reviewer: H.Niemi

60G10 Stationary stochastic processes
28D05 Measure-preserving transformations
Full Text: DOI
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