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Diskretnaya Matematika, 2014, Volume 26, Issue 3, Pages 79–89
DOI: https://doi.org/10.4213/dm1292
(Mi dm1292)
 

This article is cited in 13 scientific papers (total in 13 papers)

On repetitions of long tuples in a Markov chain

V. G. Mikhailova, A. M. Shoitovb

a Steklov Mathematical Institute of Russian Academy of Sciences
b Academy of Criptography of Russia
References:
Abstract: Let $X_0,X_1,\ldots$ be a simple ergodic finite Markov chain. We prove limit theorems for the distribution of the number $\tilde\xi(s,n)$ of events
$$\{X_{i-1}\ne X_{j-1},\ X_{i+k}= X_{j+k},\ k=0,\ldots,s-1\},\quad 1\le i<j\le n,$$
when $s,n\to\infty$. Limit theorems for distributions of some random variables connected with $\tilde\xi(s,n)$ are derived as corollaries.
Keywords: Markov chain, repetitions of tuples, Poisson limit theorem.
Received: 17.02.2014
English version:
Discrete Mathematics and Applications, 2015, Volume 25, Issue 5, Pages 295–303
DOI: https://doi.org/10.1515/dma-2015-0028
Bibliographic databases:
Document Type: Article
UDC: 519.212.2+519.214
Language: Russian
Citation: V. G. Mikhailov, A. M. Shoitov, “On repetitions of long tuples in a Markov chain”, Diskr. Mat., 26:3 (2014), 79–89; Discrete Math. Appl., 25:5 (2015), 295–303
Citation in format AMSBIB
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\by V.~G.~Mikhailov, A.~M.~Shoitov
\paper On repetitions of long tuples in a Markov chain
\jour Diskr. Mat.
\yr 2014
\vol 26
\issue 3
\pages 79--89
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\crossref{https://doi.org/10.4213/dm1292}
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\transl
\jour Discrete Math. Appl.
\yr 2015
\vol 25
\issue 5
\pages 295--303
\crossref{https://doi.org/10.1515/dma-2015-0028}
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84949970668}
Linking options:
  • https://www.mathnet.ru/eng/dm1292
  • https://doi.org/10.4213/dm1292
  • https://www.mathnet.ru/eng/dm/v26/i3/p79
  • This publication is cited in the following 13 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Дискретная математика
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