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Nearest-neighbour systems: a lemma with application to Bartlett's global solutions

Published online by Cambridge University Press:  14 July 2016

J. E. Besag
J. E. Besag*
Affiliation:
University of Liverpool
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Abstract

Bartlett has proposed two alternative forms of spatial-temporal Markov model, each leading to the standard spatial equilibrium distribution for nearest-neighbour systems on a multi-dimensional lattice. The validity of one of these forms is discussed with the aid of a lemma.

Keywords

NEAREST NEIGHBOUR CORRELATIONSGLOBAL SOLUTIONS
Type
Short Communications
Information
Journal of Applied Probability , Volume 9 , Issue 2 , June 1972 , pp. 418 - 421
Copyright
Copyright © Applied Probability Trust 1972 

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References

Bartlett, M. S. (1971) Physical nearest-neighbour models and non-linear time series, I. J. Appl. Prob. 8, 222–232.Google Scholar
Bartlett, M. S. (1972) Physical nearest-neighbour models and non-linear time series, II. Further discussion of approximate solutions and exact equations. J. Appl. Prob. 9, 76–86.CrossRefGoogle Scholar