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 Teor. Veroyatnost. i Primenen.: Year: Volume: Issue: Page: Find

 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:

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}