Markovianity of the invariant distribution of probabilistic cellular automata on the line

Jérôme Casse and Jean-François Marckert

Stochastic Processes and their Applications, 2015, vol. 125, issue 9, 3458-3483

Abstract: We revisit the problem of finding the conditions under which synchronous probabilistic cellular automata indexed by the line Z, or the periodic line Z/nZ, depending on 2 neighbours, admit as invariant distribution the law of a space-indexed Markov chain. Our advances concern PCA defined on a finite alphabet, where most of existing results concern size 2 alphabet.

Keywords: Probabilistic cellular automata; Invariant distribution (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:125:y:2015:i:9:p:3458-3483

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DOI: 10.1016/j.spa.2015.05.001

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