This article is cited in 2 papers

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 $\theta$.

Received: 31.01.1969

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

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