The Annals of Probability

An Algebraic Construction of a Class of One-Dependent Processes

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

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Abstract

A special class of stationary one-dependent two-valued stochastic processes is defined. We associate to each member of this class two parameter values, whereby different members receive different parameter values. For any given values of the parameters, we show how to determine whether: 1. a process exists having the given parameter values, and if so, 2. this process can be obtained as a two-block factor from an independent process. This determines a two-parameter subfamily of the class of stationary one-dependent two-valued stochastic processes which are not two-block factors of independent processes.

Article information

Source
Ann. Probab., Volume 17, Number 1 (1989), 128-143.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176991499

Digital Object Identifier
doi:10.1214/aop/1176991499

Mathematical Reviews number (MathSciNet)
MR972778

Zentralblatt MATH identifier
0681.60038

JSTOR
links.jstor.org

Subjects
Primary: 60G10: Stationary processes
Secondary: 28D05: Measure-preserving transformations 54H20: Topological dynamics [See also 28Dxx, 37Bxx]

Keywords
Stationary process one-dependence $m$-dependence block factors cylinder functions dynamical systems

Citation

Aaronson, Jon; Gilat, David; Keane, Michael; de Valk, Vincent. An Algebraic Construction of a Class of One-Dependent Processes. Ann. Probab. 17 (1989), no. 1, 128--143. doi:10.1214/aop/1176991499. https://projecteuclid.org/euclid.aop/1176991499


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