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Probl. Peredachi Inf., 1975, Volume 11, Issue 1, Pages 72–79 (Mi ppi1573)  

Large Systems

Ergodic Theorem for a Class of Markov Processes with Local Interaction

R. K. Romanovskii


Abstract: A necessary and sufficient condition is found for the existence of a “steady state” for certain locally interacting Markov process. This condition is formulated in terms of the “joint spectrum” of $n$ stochastic matrices controlling the process. In the case $n=1$ it coincides with the ergodic theorem for a homogeneous Markov chain.

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English version:
Problems of Information Transmission, 1975, 11:1, 57–62

Bibliographic databases:

UDC: 621.391.1:519.37
Received: 26.06.1974

Citation: R. K. Romanovskii, “Ergodic Theorem for a Class of Markov Processes with Local Interaction”, Probl. Peredachi Inf., 11:1 (1975), 72–79; Problems Inform. Transmission, 11:1 (1975), 57–62

Citation in format AMSBIB
\Bibitem{Rom75}
\by R.~K.~Romanovskii
\paper Ergodic Theorem for a~Class of Markov Processes with Local Interaction
\jour Probl. Peredachi Inf.
\yr 1975
\vol 11
\issue 1
\pages 72--79
\mathnet{http://mi.mathnet.ru/ppi1573}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=443089}
\zmath{https://zbmath.org/?q=an:0367.60114}
\transl
\jour Problems Inform. Transmission
\yr 1975
\vol 11
\issue 1
\pages 57--62


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