An algebraic construction of a class of one-dependent processes. (English) Zbl 0681.60038

Aaronson, Jon; Gilat, David; Keane, Michael; de Valk, Vincent

Ann. Probab. 17, No. 1, 128-143 (1989).

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

MSC:

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

Keywords:

algebraic construction; stationary one-dependent two-valued stochastic processes; two-block factors