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 Teor. Veroyatnost. i Primenen.: Year: Volume: Issue: Page: Find

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

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.

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

Bibliographic databases:

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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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
2. A. L. Rukhin, “Pattern correlation matrices for Markov sequences and tests of randomness”, Theory Probab. Appl., 51:4 (2007), 663–679
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