Hostname: page-component-78c5997874-s2hrs Total loading time: 0 Render date: 2024-11-05T09:56:05.542Z Has data issue: false hasContentIssue false

Rumination on Infinite Markov Systems

Published online by Cambridge University Press:  05 September 2017

Abstract

Recent work by Moussouris [10] has clarified our present knowledge of finite Markov fields. The present note examines, in a loose and general fashion, whether one can extend the treatment to infinite fields.

Type
Part V — Stochastic Processes
Copyright
Copyright © 1975 Applied Probability Trust 

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

[1] Bartlett, M. S. (1968) A further note on nearest-neighbour models. J. R. Statist. Soc. A 131, 579580.Google Scholar
[2] Bartlett, M. S. (1971) Physical nearest-neighbour models and non-linear time series. J. Appl. Prob. 8, 222232.CrossRefGoogle Scholar
[3] Bartlett, M. S. (1971) Two-dimensional nearest-neighbour systems and their ecological applications. Statistical Ecology 1, 179194.Google Scholar
[4] Bartlett, M. S. (1974) The statistical analysis of spatial pattern. Adv. Appl. Prob. 6, 336358.CrossRefGoogle Scholar
[5] Besag, J. E. (1974) Spatial interaction and the statistical analysis of lattice systems. J. R. Statist. Soc. B. 36, 192236.Google Scholar
[6] Lévy, P. (1948) Chaînes doubles de Markoff et fonctions aléatoires de deux variables. C. R. Acad. Sci. Paris 226, 5355.Google Scholar
[7] Lévy, P. (1948) Exemples de processus doubles de Markoff. C. R. Acad. Sci. Paris 226, 307308.Google Scholar
[8] Lévy, P. (1949) Processus doubles de Markoff. Colloques Internat. du Centre National de la Recherche Scientifique, Paris 13, 5359.Google Scholar
[9] Moran, P. A. P. (1973) A Gaussian-Markovian process on a square lattice. J. Appl. Prob. 10, 5462.Google Scholar
[10] Moussouris, J. (1974) Gibbs and Markov random systems with constraints. J. Statist. Phys. 10, 1133.CrossRefGoogle Scholar
[11] Rota, G. C. (1964) On the foundations of combinatorial theory. Z. Wahrscheinlichkeitsth. 2, 340368.Google Scholar