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.
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Bibliography
Berge, C., 1962,The Theory of Graphs and its Applications, Wiley, New York.
Doob, J. L., 1953,Stochastic Processes, Wiley, New York.
Feller, W., 1950,Probability Theory and Applications, Wiley, New York.
Kemeny, J. C. and Snell, J. L., 1960,Finite Markov Chains, Van Nostrand, Princeton.
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The paper is based on part of the author’s work towards the D. Sc. degree.
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Paz, A. Graph-theoretic and algebraic characterizations of some Markov processes. Israel J. Math. 1, 169–180 (1963). https://doi.org/10.1007/BF02759706
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DOI: https://doi.org/10.1007/BF02759706