Work

One-dimensional Markov random fields, Markov chains and topological Markov fields

Year: 2013

Type: article

Abstract: A topological Markov chain is the support of an ordinary first-order Markov chain. We develop the concept of topological Markov field (TMF), which is the support of a Markov random field. Using this, we show that any one-dimensional (discrete-time, finite-alphabet) stationary Markov random field must be a stationary Markov chain, and we give a version of this result for continuous-time processes. We also give a general finite procedure for deciding if a given shift space is a TMF.

Source: Proceedings of the American Mathematical Society

DOI: 10.1090/s0002-9939-2013-11741-7

Authors: Nishant Chandgotia, Guangyue Han, Brian Marcus, Tom Meyerovitch, Ronnie Pavlov

Institutions: University of British Columbia, University of Hong Kong, Ben-Gurion University of the Negev, University of Denver

Language: English

Topic: Mathematical Dynamics and Fractals

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W2002437441

FWCI: 1.502

Cites: 10

Cited by: 17

Related to: 10