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1 results

  • Unilateral Markov fields

  • David K. Pickard
  • Journal:
    Advances in Applied Probability / Volume 12 / Issue 3 / September 1980
    Published online by Cambridge University Press:
    01 July 2016, pp. 655-671
    Print publication:
    September 1980

  • 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.