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Problemy Peredachi Informatsii, 1973, Volume 9, Issue 4, Pages 66–70 (Mi ppi924)  

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
Bibliographic databases:
Document Type: Article
UDC: 621.391.1, 62-507
Language: Russian
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
Citation in format AMSBIB
\Bibitem{Rot73}
\by A.~R.~Rotenberg
\paper Asymptotic Enlargement of the States of Certain Stochastic Automata
\jour Probl. Peredachi Inf.
\yr 1973
\vol 9
\issue 4
\pages 66--70
\mathnet{http://mi.mathnet.ru/ppi924}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=379093}
\zmath{https://zbmath.org/?q=an:0318.94049}
\transl
\jour Problems Inform. Transmission
\yr 1973
\vol 9
\issue 4
\pages 321--324
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