Graph-theoretic and algebraic characterizations of some Markov processes
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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.
KeywordsStochastic Matrix Finite Graph Stochastic Matrice Algebraic Characterization Stationary Markov Chain
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