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Diskr. Mat., 1997, Volume 9, Issue 1, Pages 12–29 (Mi dm452)  

This article is cited in 12 scientific papers (total in 12 papers)

On the asymptotics of moments of the number of nonappearing $s$-chains

M. I. Tikhomirova, V. P. Chistyakov


Abstract: In this paper we investigate the asymptotic behaviour of the number $\mu_0(B)$ of the $s$-tuples from the set $B\subset\{(i_1…  i_s)\colon 1\le i_k\le N, k=1,…,s\}$ which do not occur in the polynomial scheme with outcomes $1,2,…,N$. We assume that $s$ is fixed, and the number of trials and the outcome probabilities lie in the central domain. We give asymptotic formulae for $\mathsf E\mu_0(B)$, $\mathsf E\mu_0(B)(\mu_0(B)-1)$ and $\mathsf D\mu_0(B)$. For a wide class of the sets $B$, we establish the asymptotic normality of $\mu_0(B)$.
This work was supported by the Russian Foundation for Basic Research, grant 96-01-00531.

DOI: https://doi.org/10.4213/dm452

Full text: PDF file (1228 kB)

English version:
Discrete Mathematics and Applications, 1997, 7:1, 13–32

Bibliographic databases:

UDC: 519.2
Received: 02.04.1996

Citation: M. I. Tikhomirova, V. P. Chistyakov, “On the asymptotics of moments of the number of nonappearing $s$-chains”, Diskr. Mat., 9:1 (1997), 12–29; Discrete Math. Appl., 7:1 (1997), 13–32

Citation in format AMSBIB
\Bibitem{TikChi97}
\by M.~I.~Tikhomirova, V.~P.~Chistyakov
\paper On the asymptotics of moments of the number of nonappearing $s$-chains
\jour Diskr. Mat.
\yr 1997
\vol 9
\issue 1
\pages 12--29
\mathnet{http://mi.mathnet.ru/dm452}
\crossref{https://doi.org/10.4213/dm452}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1454176}
\zmath{https://zbmath.org/?q=an:0898.60015}
\transl
\jour Discrete Math. Appl.
\yr 1997
\vol 7
\issue 1
\pages 13--32


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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. Rukhin A.L., “Distribution of the number of words with a prescribed frequency and tests of randomness”, Advances in Applied Probability, 34:4 (2002), 775–797  crossref  mathscinet  zmath  isi  scopus
    2. V. G. Mikhailov, A. M. Shoitov, “Structural equivalence of $s$-tuples in random discrete sequences”, Discrete Math. Appl., 13:6 (2003), 541–568  mathnet  crossref  crossref  mathscinet  zmath
    3. 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
    4. M. I. Tikhomirova, “Limit distributions of the number of absent chains of identical outcomes”, Discrete Math. Appl., 18:3 (2008), 293–300  mathnet  crossref  crossref  mathscinet  zmath  elib
    5. M. I. Tikhomirova, “Asymptotic normality of the number of absent noncontinuous chains of outcomes of independent trials”, Discrete Math. Appl., 19:3 (2009), 293–308  mathnet  crossref  crossref  mathscinet  elib
    6. V. P. Chistyakov, “Asymptotic normality of the number of values of $m$-dependent random variables which occur a given number of times”, Discrete Math. Appl., 21:1 (2011), 23–37  mathnet  crossref  crossref  mathscinet  elib
    7. M. I. Tikhomirova, V. P. Chistyakov, “Asimptoticheskaya normalnost chisla nepoyavivshikhsya znachenii $m$-zavisimykh sluchainykh velichin”, Matem. vopr. kriptogr., 2:1 (2011), 119–129  mathnet  crossref
    8. M. I. Tikhomirova, V. P. Chistyakov, “Asymptotic normality of numbers of non-occurring values of $m$-dependent random variables”, Discrete Math. Appl., 24:5 (2014), 305–317  mathnet  crossref  crossref  mathscinet  elib
    9. V. P. Chistyakov, “On the asymptotic normality of the number of empty cells in a scheme of group allocation of particles”, Discrete Math. Appl., 24:6 (2014), 319–325  mathnet  crossref  crossref  mathscinet  elib  elib
    10. V. P. Chistyakov, “Ob asimptoticheskoi normalnosti chisla pustykh yacheek v odnoi skheme razmescheniya chastits komplektami”, Matem. vopr. kriptogr., 5:4 (2014), 129–138  mathnet  crossref
    11. M. I. Tikhomirova, V. P. Chistyakov, “On the asymptotic normality of some sums of dependent random variables”, Discrete Math. Appl., 27:2 (2017), 123–129  mathnet  crossref  crossref  mathscinet  isi  elib
    12. Masol I V. Popereshnyak V S., “Checking the Randomness of Bits Disposition in Local Segments of the (0,1)-Sequence”, Cybern. Syst. Anal., 56:3 (2020), 513–520  crossref  isi
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