Hostname: page-component-78c5997874-fbnjt Total loading time: 0 Render date: 2024-11-03T00:37:02.405Z Has data issue: false hasContentIssue false
  • English
  • Français

Further properties for unilateral binary processes

Published online by Cambridge University Press:  14 July 2016

R. F. Galbraith  and
D. Walley
R. F. Galbraith*
Affiliation:
University College London
D. Walley
Affiliation:
University College London
*
∗ Postal address: Department of Statistical Science, University College London, Gower St, London WC1E 6BT, U.K.
Get access Rights & Permissions [Opens in a new window]

Abstract

Results and methods discussed in two previous papers are extended to other cases. Comparison is made with recent work by Pickard (1980) and an earlier conjecture is disproved.

Keywords

BINARY VARIABLESCORRELATION FUNCTIONERGODICITYTWO-DIMENSIONAL PROCESSUNILATERAL PROCESS
Type
Research Papers
Information
Journal of Applied Probability , Volume 19 , Issue 2 , June 1982 , pp. 332 - 343
Copyright
Copyright © Applied Probability Trust 1982 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Besag, J. E. (1972) On the correlation structure of some two-dimensional stationary processes. Biometrika 59, 43–48.CrossRefGoogle Scholar
Besag, J. E. (1974) Spatial interaction and the statistical analysis of lattice systems. J. R. Statist. Soc. B 36, 192–225.Google Scholar
Enting, I. G. (1977) Crystal growth models and Ising models. J. Phys. C 10, 1379–1388.CrossRefGoogle Scholar
Galbraith, R. F. and Walley, D. (1976) On a two-dimensional binary process. J. Appl. Prob. 13, 548–557.CrossRefGoogle Scholar
Galbraith, R. F. and Walley, D. (1980) Ergodic properties of a two-dimensional binary process. J. Appl. Prob. 17, 124–133.CrossRefGoogle Scholar
Miller, G. H. and Welberry, T. R. (1979) A three-dimensional model of crystal-growth disorder. Acta Cryst. A 35, 391–400.CrossRefGoogle Scholar
Pickard, D. K. (1977) A curious binary lattice process. J. Appl. Prob. 14, 717–731.CrossRefGoogle Scholar
Pickard, D. K. (1978) Unilateral Ising models. Suppl. Adv. Appl. Prob. 10, 57–64.CrossRefGoogle Scholar
Pickard, D. K. (1980) Unilateral Markov fields. Adv. Appl. Prob. 12, 655–671.CrossRefGoogle Scholar
Welberry, T. R. (1977) Solution of crystal growth disorder models by imposition of symmetry. Proc. R. Soc. London A 353, 363–376.Google Scholar
Welberry, T. R. and Galbraith, R. F. (1975) The effect of non-linearity on a two-dimensional model of crystal growth disorder. J. Appl. Cryst. 8, 636–644.CrossRefGoogle Scholar
Welberry, T. R. and Miller, G. H. (1977) An approximation to a two-dimensional binary process. J. Appl. Prob. 14, 862–868.CrossRefGoogle Scholar