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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

##### MSC:
 60G10 Stationary stochastic processes 28D05 Measure-preserving transformations
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