Unilateral Markov fields
- 1 September 1980
- journal article
- Published by Cambridge University Press (CUP) in Advances in Applied Probability
- Vol. 12 (3) , 655-671
- https://doi.org/10.2307/1426425
Abstract
Recently, there has been considerable interest in some specialized binary lattice processes. However, this exciting work has been rather fragmentary and heuristic. Rigorous proofs are provided for the existence of some classes of stationary unilateral Markov fields on infinite square lattices. (Neighbours are sites which are horizontally, vertically, or diagonally adjacent.) Many of the difficulties are avoided by characterizing stationary unilateral Markov fields on finite lattices first. Detailed analyses are given for both binary and Gaussian variables.Keywords
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