Hostname: page-component-78c5997874-v9fdk Total loading time: 0 Render date: 2024-11-08T15:32:10.724Z Has data issue: false hasContentIssue false
  • English
  • Français

Limiting second moments for transient states of Markov chains

Published online by Cambridge University Press:  14 July 2016

H. P. Wynn
H. P. Wynn*
Affiliation:
University of Kent at Canterbury
Get access Rights & Permissions [Opens in a new window]

Abstract

The set of transient states of a Markov chain is considered as a system. If numbers of arrivals to the system at discrete time points have constant mean and covariance matrix then there is a limiting distribution of numbers in the states. Necessary and sufficient conditions are given for this distribution to yield zero correlations between states.

Keywords

MARKOV CHAINSTRANSIENT STATESPOISSON ARRIVALS
Type
Short Communications
Information
Journal of Applied Probability , Volume 10 , Issue 4 , December 1973 , pp. 891 - 894
Copyright
Copyright © Applied Probability Trust 1973 

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

Bartholomew, D. J. (1967) Stochastic Models for Social Processes. Wiley, New York.Google Scholar
Bartlett, M. S. (1949) Some evolutionary stochastic processes. J. R. Statist. Soc. B 11, 211–229.Google Scholar
Derman, C. (1955) Some contributions to the theory of denumerable Markov chains. Trans. Amer. Math. Soc. 79, 541–555.Google Scholar
Harris, T. E. (1963) The Theory of Branching Processes. Springer-Verlag, Berlin.Google Scholar
Kingman, J. F. C. (1969) Markov population processes. J. Appl. Prob. 6, 1–18.Google Scholar
Pollard, J. H. (1967) Hierarchical population models with Poisson recruitment. J. Appl. Prob. 4, 209–213.Google Scholar