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
SN - 0002-9939
VL - 142
SP - 227
EP - 242
JO - Proceedings of the American Mathematical Society
JF - Proceedings of the American Mathematical Society
IS - 1
ER -