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Teor. Veroyatnost. i Primenen., 1970, Volume 15, Issue 3, Pages 536–540 (Mi tvp1863)  

Short Communications

Correlation equations for the stable measure of a Markov chain

N. B. Vasil'ev

Moscow

Abstract: Each lamp of an infinite garland lights up with probability 1 if it and its neighbour both were lighting at the previous time moment, and with probability $\theta$ in the other case. It is shown that except for the trivial stable state “all the lamps are lighting”, for small $\theta$ there is only one stable probability measure $P_\theta$ on the state space of such systems and $P_\theta$ depends analitically on $\theta$.

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English version:
Theory of Probability and its Applications, 1970, 15:3, 521–525

Bibliographic databases:

Received: 31.01.1969

Citation: N. B. Vasil'ev, “Correlation equations for the stable measure of a Markov chain”, Teor. Veroyatnost. i Primenen., 15:3 (1970), 536–540; Theory Probab. Appl., 15:3 (1970), 521–525

Citation in format AMSBIB
\Bibitem{Vas70}
\by N.~B.~Vasil'ev
\paper Correlation equations for the stable measure of a~Markov chain
\jour Teor. Veroyatnost. i Primenen.
\yr 1970
\vol 15
\issue 3
\pages 536--540
\mathnet{http://mi.mathnet.ru/tvp1863}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=286179}
\zmath{https://zbmath.org/?q=an:0205.45002}
\transl
\jour Theory Probab. Appl.
\yr 1970
\vol 15
\issue 3
\pages 521--525
\crossref{https://doi.org/10.1137/1115056}


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