Hostname: page-component-cd9895bd7-gvvz8 Total loading time: 0 Render date: 2024-12-26T18:27:47.361Z Has data issue: false hasContentIssue false

Synchronous and Asynchronous Reversible Markov Systems(1)

Published online by Cambridge University Press:  20 November 2018

D. A. Dawson*
Affiliation:
Carleton University, Ottawa, Canada
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The relationships between synchronous and asynchronous reversible Markov systems are investigated. It is shown that the invariant measure of such systems is a second order Markov random field. The conditions under which the invariant measure is a first order Markov random field are obtained.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1975

Footnotes

(1)

This research was supported by the National Research Council of Canada.

References

1. Averintzev, M. B., On a method of describing discrete parameter random fields, Problemy Peredaci Informacii (6), 1970, 100109.Google Scholar
2. Dawson, D. A., Information flow in discrete Markov systems, to appear in J. Appl. Prob.Google Scholar
3. Dobrushin, R. L., The description of a random field by means of conditional probabilities and conditions of its regularity, Th. Prob. Appl. (13), 1968, 197224.Google Scholar
4. Kindermann, R. P., Random fields; theorems and examples, J. Undergraduate Mathematics (5), 1973, 2534.Google Scholar
5. Spitzer, F., Random fields and interacting particle systems, Summer Seminar Notes, M.A.A., 1971.Google Scholar