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Mat. Vopr. Kriptogr., 2015, Volume 6, Issue 3, Pages 117–133 (Mi mvk163)  

This article is cited in 3 scientific papers (total in 3 papers)

On multiple repetitions of long tuples in a Markov chain

V. G. Mikhailova, A. M. Shoitovb

a Steklov Mathematical Institute of RAS, Moscow
b Academy of Cryptography of the Russian Federation, Moscow

Abstract: Let $X_0,X_1,…$ be a simple ergodic Markov chain with $N$ states and $\tilde\xi_{n,k}^{(m)}(s)$ be the number of $m$-series of $k$-repetitions of $s$-tuples in the chain segment $X_0,X_1,…,X_{n+s+m}$. The sufficient conditions for the distribution of the vector $\tilde\Xi_{n,k,M}(s)=(\tilde\xi_{n,k}^{(1)}(s),…,\tilde\xi_{n,k}^{(M)}(s))$ to converge to the multidimensional Poisson distribution are found. This permits to prove limit theorems for the distributions of some random variables connected with $\tilde\Xi_{n,k,M}(s)$.

Key words: Markov chain, multiple repetitions of tuples, multidimensional Poisson limit theorem.

DOI: https://doi.org/10.4213/mvk163

Full text: PDF file (152 kB)
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Bibliographic databases:

Document Type: Article
UDC: 519.212.2+519.214
Received 02.VI.2015

Citation: V. G. Mikhailov, A. M. Shoitov, “On multiple repetitions of long tuples in a Markov chain”, Mat. Vopr. Kriptogr., 6:3 (2015), 117–133

Citation in format AMSBIB
\Bibitem{MikSho15}
\by V.~G.~Mikhailov, A.~M.~Shoitov
\paper On multiple repetitions of long tuples in a~Markov chain
\jour Mat. Vopr. Kriptogr.
\yr 2015
\vol 6
\issue 3
\pages 117--133
\mathnet{http://mi.mathnet.ru/mvk163}
\crossref{https://doi.org/10.4213/mvk163}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3540249}
\elib{http://elibrary.ru/item.asp?id=25064794}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. N. M. Mezhennaya, “O chisle sovpadenii znakov v diskretnoi sluchainoi posledovatelnosti, upravlyaemoi tsepyu Markova”, Sib. elektron. matem. izv., 13 (2016), 305–317  mathnet  crossref
    2. V. G. Mikhailov, “On the probability of existence of substrings with the same structure in a random sequence”, Discrete Math. Appl., 27:6 (2017), 377–386  mathnet  crossref  crossref  mathscinet  isi  elib
    3. V. G. Mikhailov, “On the reduction property of the number of $H$-equivalent tuples of states in a discrete Markov chain”, Discrete Math. Appl., 28:2 (2018), 75–82  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
  • Математические вопросы криптографии
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