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Teor. Veroyatnost. i Primenen., 1965, Volume 10, Issue 3, Pages 547–551 (Mi tvp553)  

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

Short Communications

On the probability of the non-appearence of a given number of $s$-tuples in compound Markov chains

P. F. Belyaev

Moscow

Abstract: Let $\{j_r\}$, $r=\overline{1,n}$, $j_r=\overline{1,k}$ be a sequence obtained by realizations of $n$ trials which are bound into a compound Markov chain of order $s$ with $k$ outcomes.
Let $s$-tuple denote a subsequence of $\{j_r\}$ consisting of $s$ consecutive symbols and let $P(n,k;m)$ be the probability that in the sequence $\{j_r\}$ of all possible $k^s$ $s$-tuples exactly $m$ $s$-tuples are missing.
The asymptotic behaviour of the probability $P(n,k;m)$ as $n\to\infty$; $k\to\infty$; $k^re^{-n/k^s}<c<\infty$ is considered.

Full text: PDF file (962 kB)

English version:
Theory of Probability and its Applications, 1965, 10:3, 496–499

Bibliographic databases:

Received: 24.12.1964

Citation: P. F. Belyaev, “On the probability of the non-appearence of a given number of $s$-tuples in compound Markov chains”, Teor. Veroyatnost. i Primenen., 10:3 (1965), 547–551; Theory Probab. Appl., 10:3 (1965), 496–499

Citation in format AMSBIB
\Bibitem{Bel65}
\by P.~F.~Belyaev
\paper On the probability of the non-appearence of a~given number of $s$-tuples in compound Markov chains
\jour Teor. Veroyatnost. i Primenen.
\yr 1965
\vol 10
\issue 3
\pages 547--551
\mathnet{http://mi.mathnet.ru/tvp553}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=193665}
\zmath{https://zbmath.org/?q=an:0168.16301}
\transl
\jour Theory Probab. Appl.
\yr 1965
\vol 10
\issue 3
\pages 496--499
\crossref{https://doi.org/10.1137/1110061}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. M. Zubkov, “Inequalities for transition probabilities with taboos and their applications”, Math. USSR-Sb., 37:4 (1980), 451–488  mathnet  crossref  mathscinet  zmath  isi
    2. A. L. Rukhin, “Pattern correlation matrices for Markov sequences and tests of randomness”, Theory Probab. Appl., 51:4 (2007), 663–679  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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