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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
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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 

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