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Problemy Peredachi Informatsii, 1973, Volume 9, Issue 4, Pages 66–70
(Mi ppi924)
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Automata Theory
Asymptotic Enlargement of the States of Certain Stochastic Automata
A. R. Rotenberg
Abstract:
Let a homogeneous Markov chain having a finite number of states and describing a stochastic automaton depend on a parameter $\varepsilon$ in such a way that the transition probabilities are continuous functions of $\varepsilon$ for $\varepsilon=\varepsilon_0$ and the set of states of the chain for $\varepsilon=\varepsilon_0$ decomposes into the union of $k>1$ ergodic sets $X_1,\dots,X_k$. A family of Markov processes describing a random walk of the original Markov process on the sets $X_1,\dots,X_k$ as $\varepsilon\to\varepsilon_0$ is constructed.
Received: 06.05.1972 Revised: 06.10.1972
Citation:
A. R. Rotenberg, “Asymptotic Enlargement of the States of Certain Stochastic Automata”, Probl. Peredachi Inf., 9:4 (1973), 66–70; Problems Inform. Transmission, 9:4 (1973), 321–324
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https://www.mathnet.ru/eng/ppi924 https://www.mathnet.ru/eng/ppi/v9/i4/p66
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Abstract page: | 172 | Full-text PDF : | 81 |
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