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Positive columns for stochastic matrices

Published online by Cambridge University Press:  14 July 2016

Dean Isaacson  and
Richard Madsen
Dean Isaacson
Affiliation:
Iowa State University, Ames
Richard Madsen
Affiliation:
University of Missouri, Columbia
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Abstract

If an n × n stochastic matrix has a column with no zeros, one can immediately conclude that the chain is ergodic and the state corresponding to that column is persistent and aperiodic. In this paper it is shown that it is decidable whether or not some power of a finite stochastic matrix has a positive column. Some problems regarding positive columns in infinite stochastic matrices are also considered.

Keywords

STATIONARY MARKOV CHAINSDECIDABILITYERGODIC COEFFICIENTSTOCHASTIC MATRIXIRREDUCIBLEAPERIODICPERSISTENTPRIMITIVE
Type
Short Communications
Information
Journal of Applied Probability , Volume 11 , Issue 4 , December 1974 , pp. 829 - 835
Copyright
Copyright © Applied Probability Trust 1974 

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References

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