Hostname: page-component-848d4c4894-nmvwc Total loading time: 0 Render date: 2024-06-25T00:30:06.832Z Has data issue: false hasContentIssue false
  • English
  • Français

The inverse problem in reducible Markov chains

Published online by Cambridge University Press:  14 July 2016

W. D. Ray  and
F. Margo
W. D. Ray
Affiliation:
Birkbeck College London
F. Margo
Affiliation:
Albright and Wilson Ltd., London
Get access Rights & Permissions [Opens in a new window]

Abstract

The equilibrium probability distribution over the set of absorbing states of a reducible Markov chain is specified a priori and it is required to obtain the constrained sub-space or feasible region for all possible initial probability distributions over the set of transient states. This is called the inverse problem. It is shown that a feasible region exists for the choice of equilibrium distribution. Two different cases are studied: Case I, where the number of transient states exceeds that of the absorbing states and Case II, the converse. The approach is via the use of generalised inverses and numerical examples are given.

Keywords

FEASIBLE REGIONSREDUCIBLE MARKOV CHAINSGENERALISED INVERSERANDOM WALKAPPLICATIONS
Type
Research Papers
Information
Journal of Applied Probability , Volume 13 , Issue 1 , March 1976 , pp. 49 - 56
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

Bartholomew, D. J. (1973) Stochastic Models for Social Processes. John Wiley and Sons, London.Google Scholar
Cox, D. R. and Miller, H. D. (1975) The Theory of Stochastic Processes. Methuen, London.Google Scholar
Jury, E. I. (1964) Theory and Application of the Z-Transform Method. John Wiley and Sons, New York.Google Scholar
Mode, C. J. (1971) Multitype Branching Processes. American Elsevier, New York.Google Scholar
Rao, C. R. (1965) Linear Statistical Inference and its Applications. John Wiley and Sons, New York.Google Scholar
Ray, W. D. (1975) Specifying absorption probabilities for the simple random walk. Stoch. Proc. Appl. To appear.Google Scholar
Stone, R. (1972) A Markovian education model and other examples linking social behaviour to the economy. J. R. Statist. Soc. A 135, 511–544.Google Scholar