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A note on the inverse problem for reducible Markov chains

Published online by Cambridge University Press:  14 July 2016

A. O. Pittenger
A. O. Pittenger*
Affiliation:
University of Maryland, Baltimore County
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Abstract

Suppose a physical process is modelled by a Markov chain with transition probability on S 1 ∪ S 2, S 1 denoting the transient states and S 2 a set of absorbing states.

If v denotes the output distribution on S 2, the question arises as to what input distributions (of raw materials) on S 1 produce v. In this note we give an alternative to the formulation of Ray and Margo [2] and reduce the problem to one system of linear inequalities. An application to random walk is given and the equiprobability case examined in detail.

Keywords

DISCRETE-TIME MARKOV CHAINSHITTING TIMESINVERSE BOUNDARY VALUE PROBLEM

Information

Type
Short Communications
Information
Journal of Applied Probability , Volume 14 , Issue 3 , September 1977 , pp. 621 - 625
Copyright
Copyright © Applied Probability Trust 1977 

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References

[1] Balinski, M. L. (1961) An algorithm for finding all vertices of convex polyhedral sets. SIAM J. 9, 72–88.Google Scholar
[2] Ray, W. D. and Margo, F. (1976) The inverse problem in reducible Markov chains. J. Appl. Prob. 13, 49–56.CrossRefGoogle Scholar
[3] Ray, W. D. (1976) Specifying absorption probabilities for simple random walk. Stoch. Proc. Appl. 4, 243–252.CrossRefGoogle Scholar