Hostname: page-component-586b7cd67f-t7fkt Total loading time: 0 Render date: 2024-11-24T00:43:18.821Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Dobrushin, R. L. (1956) Central limit theorems for non-stationary Markov chains II. Theor. Probability Appl. 1, 329–383.Google Scholar
Isaacson, D. and Sposito, V. (1973) Analyzing a Markov chain on a computer. Submitted.Google Scholar
Paz, A. (1963) Graph-theoretic and algebraic characterizations of some Markov processes. Israel J. Math. 3, 169–180.Google Scholar
Paz, A. (1971) Introduction to Probabilistic Automata. Academic Press, New York.Google Scholar
Perkins, P. (1961) A theorem on regular matrices. Pacific J. Math. 11, 1529–1533.Google Scholar