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Israel Journal of Mathematics

, Volume 1, Issue 3, pp 169–180 | Cite as

Graph-theoretic and algebraic characterizations of some Markov processes

Article

Abstract

An algebraic decidable condition for a stationary Markov chain to consist of a single ergodic set, and a graph-theoretic decidable condition for a stationary Markov chain to consist of a single ergodic noncyclic set are formulated.

In the third part of the paper a graph-theoretic condition for a nonstationary Markov chain to have the weakly-ergodic property is given.

Keywords

Stochastic Matrix Finite Graph Stochastic Matrice Algebraic Characterization Stationary Markov Chain 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Bibliography

  1. 1.
    Berge, C., 1962,The Theory of Graphs and its Applications, Wiley, New York.MATHGoogle Scholar
  2. 2.
    Doob, J. L., 1953,Stochastic Processes, Wiley, New York.MATHGoogle Scholar
  3. 3.
    Feller, W., 1950,Probability Theory and Applications, Wiley, New York.MATHGoogle Scholar
  4. 4.
    Kemeny, J. C. and Snell, J. L., 1960,Finite Markov Chains, Van Nostrand, Princeton.MATHGoogle Scholar

Copyright information

© Hebrew University 1963

Authors and Affiliations

  • A. Paz
    • 1
  1. 1.Technion-Israel Institute of TechnologyHaifa

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