Hostname: page-component-78c5997874-j824f Total loading time: 0 Render date: 2024-11-10T19:23:20.712Z Has data issue: false hasContentIssue false
  • English
  • Français

Representation of denumerable Markov chains with multiple states by weighted circuits

Published online by Cambridge University Press:  14 July 2016

S. Kalpazidou
S. Kalpazidou*
Affiliation:
Aristotle University of Thessaloniki
*
∗Postal address: Department of Mathematics, Aristotle University of Thessaloniki, 54006 Thessaloniki, Greece.
Get access Rights & Permissions [Opens in a new window]

Abstract

The constructive solution to the problem of representing a strictly stationary Markov chain ζ with a countable infinity of r-sequences (i1, i2, · ··, ir), r > 1, as states by a class of directed weighted circuits is given. Associating the chain ζ with its dual chain η having reversed states and the same transition law, a connection with physical laws that govern diffusion of electrical current through a directed planar network with r-series-connected nodes is shown.

Keywords

STATIONARITYROLLING-CIRCUITS
Type
Research Papers
Information
Journal of Applied Probability , Volume 26 , Issue 1 , March 1989 , pp. 23 - 35
Copyright
Copyright © Applied Probability Trust 1989 

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] Doyle, P. G. and Snell, J. L. (1984) Random Walks and Electric Networks. The Carus Mathematical Monographs Nr. 22.CrossRefGoogle Scholar
[2] Iosifescu, M. (1965) Sur l'ergodicité uniforme des chaînes de Markoff variables et multiples. C. R. Acad. Sci. Paris 261, 875–877.Google Scholar
[3] Iosifescu, M. (1973) On multiple Markovian dependence, Proc. Fourth Conf. on Probability Theory, 1971, Brasov , Publishing House of the Romanian Academy, Bucharest, 65–71.Google Scholar
[4] Iosifescu, M. (1969) Sur les chaînes de Markov multiples. Bull. Inst. Internat. Statist. 43(2), 333–335.Google Scholar
[5] Kalpazidou, S. (1988) On the representation of finite multiple Markov chains by weighted circuits. J. Multivariate Anal. 25, 241–271.CrossRefGoogle Scholar