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This paper is concerned with infinite-state probabilistic transition tables, representing the dynamical behavior of a probabilistic automaton and nonhomogeneous infinite-state Markov chains. Many known theorems are generalized from the finite-state case to the infinite-state case. A possible application to the problem of computing, approximately, products of infinite-state stochastic matrices is outlined.
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Azaria Paz (1970) studied this question.
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