TY - JOUR

T1 - One-dimensional Markov random fields, Markov chains and topological Markov fields

AU - Chandgotia, Nishant

AU - Han, Guangyue

AU - Marcus, Brian

AU - Meyerovitch, Tom

AU - Pavlov, Ronnie

PY - 2014/1/1

Y1 - 2014/1/1

N2 - A topological Markov chain is the support of an ordinary firstorder 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.

AB - A topological Markov chain is the support of an ordinary firstorder 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.

UR - http://www.scopus.com/inward/record.url?scp=84886305570&partnerID=8YFLogxK

U2 - 10.1090/S0002-9939-2013-11741-7

DO - 10.1090/S0002-9939-2013-11741-7

M3 - Article

AN - SCOPUS:84886305570

VL - 142

SP - 227

EP - 242

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 1

ER -