Hostname: page-component-586b7cd67f-dsjbd Total loading time: 0 Render date: 2024-11-25T16:12:06.124Z Has data issue: false hasContentIssue false
  • English
  • Français

On a two-dimensional binary process

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
Get access Rights & Permissions [Opens in a new window]

Abstract

We consider a two-dimensional stochastic process of binary variables xij defined so that the conditional distribution of xij given its predecessors depends only on xi–1j and xij–1 Properties of the equilibrium distribution, when this exists, are investigated using three different representations of the process and explicit results are given in some special cases.

Keywords

TWO-DIMENSIONAL PROCESSBINARY VARIABLESMARKOV CHAINCORRELATION FUNCTIONPOWER METHOD FOR EIGENVECTORS
Type
Research Papers
Information
Journal of Applied Probability , Volume 13 , Issue 3 , September 1976 , pp. 548 - 557
Copyright
Copyright © Applied Probability Trust 1976 

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

Bartlett, M. S. (1967) Inference and stochastic processes. J. R. Statist. Soc. A 130, 467–477.Google Scholar
Bartlett, M. S. (1968) A further note on nearest neighbour models. J. R. Statist. Soc. A 181, 579–588.Google Scholar
Bartlett, M. S. and Besag, J. E. (1968) Correlation properties of some nearest-neighbour models. Bull. Int. Statist. Inst. 43 (2), 191–193.Google Scholar
Bartlett, M. S. (1971) Physical nearest-neighbour systems and non-linear time series. J. Appl. Prob. 8, 222–232.CrossRefGoogle Scholar
Besag, J. E. (1972) On the correlation structure of some two-dimensional stationary processes. Biometrika 59, 43–48.CrossRefGoogle Scholar
Besag, J. E. (1972) Nearest-neighbour systems and the auto-logistic model for binary data. J. R. Statist. Soc. B 34, 75–81.Google Scholar
Besag, J. E. (1974) Spatial interaction and the statistical analysis of lattice systems. J. R. Statist. Soc. B 36, 192–225.Google Scholar
Welberry, T. R. and Galbraith, R. (1973) A two-dimensional model of crystal growth disorder. J. Appl. Cryst. 6, 87–96.CrossRefGoogle Scholar