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Moscow Mathematical Journal, 2019, Volume 19, Number 1, Pages 37–50
DOI: https://doi.org/10.17323/1609-4514-2019-19-1-37-50
(Mi mmj699)
 

This article is cited in 2 scientific papers (total in 2 papers)

Topological and metric recurrence for general Markov chains

Michael Blankab

a Institute for Information Transmission Problems RAS (Kharkevich Institute), Bolshoy Karetny per. 19, build. 1, Moscow 127051 Russia
b National Research University "Higher School of Economics"
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Abstract: Using ideas borrowed from topological dynamics and ergodic theory we introduce topological and metric versions of the recurrence property for general Markov chains. The main question of interest here is how large is the set of recurrent points. We show that under some mild technical assumptions the set of non-recurrent points is of zero reference measure. Necessary and sufficient conditions for a reference measure $m$ (which needs not to be dynamically invariant) to satisfy this property are obtained. These results are new even in the purely deterministic setting.
Key words and phrases: ergodic theory, invariant measure, typical trajectory, Markov chain.
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Document Type: Article
Language: Russian
Citation: Michael Blank, “Topological and metric recurrence for general Markov chains”, Mosc. Math. J., 19:1 (2019), 37–50
Citation in format AMSBIB
\Bibitem{Bla19}
\by Michael~Blank
\paper Topological and metric recurrence for general Markov chains
\jour Mosc. Math.~J.
\yr 2019
\vol 19
\issue 1
\pages 37--50
\mathnet{http://mi.mathnet.ru/mmj699}
\crossref{https://doi.org/10.17323/1609-4514-2019-19-1-37-50}
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  • https://www.mathnet.ru/eng/mmj/v19/i1/p37
  • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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