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An algebraic construction of a class of one-dependent processes. (English) Zbl 0681.60038
A discrete-time stochastic process \((X_ n)\) is called one-dependent if at any given time n, its past \((X_ k)_{k<n}\) is independent of its future \((X_ k)_{k>n}\). In contrast to the Markovian concept, no knowledge of the present value \(X_ n\) is assumed.
An algebraic construction of stationary one-dependent two-valued stochastic processes is given which are not two-block factors of independent processes [see, e.g. S. Janson, ibid. 12, 805-816 (1984; Zbl 0545.60080 )].
Reviewer: G.Oprisian

60G10 Stationary stochastic processes
28D05 Measure-preserving transformations
54H20 Topological dynamics (MSC2010)
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