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

Chandgotia, Nishant; Han, Guangyue; Marcus, Brian; Meyerovitch, Tom; Pavlov, Ronnie

doi:10.1090/S0002-9939-2013-11741-7

One-dimensional Markov random fields, Markov chains and topological Markov fields
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by Nishant Chandgotia, Guangyue Han, Brian Marcus, Tom Meyerovitch and Ronnie Pavlov

Proc. Amer. Math. Soc. 142 (2014), 227-242

DOI: https://doi.org/10.1090/S0002-9939-2013-11741-7

Published electronically: October 3, 2013

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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.

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