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Homogeneous Markov chains by bounded transition matrix

Part of: Markov processes

Published online by Cambridge University Press:  14 July 2016

D. J. Hartfiel
D. J. Hartfiel*
Affiliation:
Texas A&M University
*
∗ Postal address: Department of Mathematics, Texas A&M University, College Station, TX 77 843–3368, USA.
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Abstract

Let A be a stochastic matrix and ε a positive number. We consider all stochastic matrices within ε of A and their corresponding stochastic eigenvectors. A convex polytope containing these vectors is described. An efficient algorithm for computing bounds on the components of these vectors is also given. The work is compared to previous such work done by the author and by Courtois and Semai.

Keywords

STOCHASTIC MATRIXAPPROXIMATION OF STOCHASTIC EIGENVECTOR

MSC classification

Primary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces)
Type
Research Papers
Information
Journal of Applied Probability , Volume 31 , Issue 2 , June 1994 , pp. 362 - 372
Copyright
Copyright © Applied Probability Trust 1994 

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References

[1] Courtois, P. J. and Semal, P. (1984) Bounds for the positive eigenvalues of nonnegative matrices and their approximations by decomposition. J. Assoc. Comput. Mach. 31, 804–825.CrossRefGoogle Scholar
[2] Gantmacher, F. R. (1964) The Theory of Matrices, Vol. 2. Chelsea, New York.Google Scholar
[3] Hartfiel, D. J. (1981) On the limiting set of stochastic products xA1 Am. Proc. Amer. Math. Soc. 81, 201–206.Google Scholar
[4] Hartfiel, D. J. (1983) Stochastic eigenvectors for qualitative stochastic matrices. Discrete Math. 43, 191–197.Google Scholar
[5] Hartfiel, D. J. (1987) Computing limits of convex sets of distribution vectors xA1Ak. J. Statist. Comput. Simul. 27, 1–15.Google Scholar
[6] Hartfiel, D. J. (1991) Component bounds for Markov set-chain limiting set. J. Statist. Comput. Simul. 38, 15–24.Google Scholar
[7] Rothblum, U. G. and Tan, C. P. (1985) Upper bounds on the maximal modulus of subdominant eigenvalues of nonnegative matrices. Linear Algebra Appl. 66, 45–86.Google Scholar
[8] Seneta, E. (1973) Non-Negative Matrices. Wiley, New York.Google Scholar
[9] Wesselkamper, T. C. (1981) Computer program schemata and processes they generate. IEEE Trans. Software Eng. 8, 412–419.Google Scholar