## The Annals of Probability

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

### An Algebraic Construction of a Class of One-Dependent Processes

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

#### 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