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Programming problems and changes in the stable behavior of a class of Markov chains

Published online by Cambridge University Press:  14 July 2016

Richard V. Evans
Richard V. Evans*
Affiliation:
University of Illinois at Urbana-Champaign
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Abstract

This paper develops expressions for the derivatives with respect to a parameter μ of the stable probabilities of a class of Markov chains whose transition matrices are of the form Q + μW. These expressions lead to iterative schemes for calculation which in turn suggest gradient algorithms for finding locally optimal chains.

Type
Research Papers
Information
Journal of Applied Probability , Volume 8 , Issue 3 , September 1971 , pp. 543 - 550
Copyright
Copyright © Applied Probability Trust 1971 

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References

[1] Evans, R. V. (1968) Programming in Markov processes. Tech. Memorandum No. 123, Department of Operations Research, Univ. of Illinois at Urbana-Champaign.Google Scholar
[2] Kumin, H. (1968) The Design of Markovian Congestion Systems. Ph.D. Thesis, Case Western Reserve University. Tech. Memorandum No. 115.Google Scholar
[3] Schweitzer, P. J. (1968) Perturbation theory and finite Markov chains. J. Appl. Prob. 5, 401–413.CrossRefGoogle Scholar