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Diskretnaya Matematika, 2004, Volume 16, Issue 3, Pages 43–62
DOI: https://doi.org/10.4213/dm162
(Mi dm162)
 

This article is cited in 10 scientific papers (total in 10 papers)

Joint distribution of the number of ones and the number of 1-runs in binary Markov sequences

L. Ja. Savel'ev, S. V. Balakin
References:
Abstract: We describe the distributions of the number of ones, the number of runs of ones in a binary Markov sequence and their joint distribution. We find the generating functions of the distributions under consideration, calculate the means, variances and covariances. For these moments we give explicit and asymptotic formulas with estimates of accuracy. Formulas for the Gaussian approximations are also derived. We consider the corresponding operator equations. In this connection we describe a special model of random walks.
This research was supported by the Russian Foundation for Basic Research, grant 02–01–0946.
Received: 12.10.2003
English version:
Discrete Mathematics and Applications, 2004, Volume 14, Issue 4, Pages 353–372
DOI: https://doi.org/10.1515/1569392041938802
Bibliographic databases:
UDC: 519.2
Language: Russian
Citation: L. Ja. Savel'ev, S. V. Balakin, “Joint distribution of the number of ones and the number of 1-runs in binary Markov sequences”, Diskr. Mat., 16:3 (2004), 43–62; Discrete Math. Appl., 14:4 (2004), 353–372
Citation in format AMSBIB
\Bibitem{SavBal04}
\by L.~Ja.~Savel'ev, S.~V.~Balakin
\paper Joint distribution of the number of ones and the number of 1-runs in binary Markov sequences
\jour Diskr. Mat.
\yr 2004
\vol 16
\issue 3
\pages 43--62
\mathnet{http://mi.mathnet.ru/dm162}
\crossref{https://doi.org/10.4213/dm162}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2109796}
\zmath{https://zbmath.org/?q=an:1103.60302}
\transl
\jour Discrete Math. Appl.
\yr 2004
\vol 14
\issue 4
\pages 353--372
\crossref{https://doi.org/10.1515/1569392041938802}
Linking options:
  • https://www.mathnet.ru/eng/dm162
  • https://doi.org/10.4213/dm162
  • https://www.mathnet.ru/eng/dm/v16/i3/p43
  • This publication is cited in the following 10 articles:
    1. N. M. Mezhennaya, “Otsenka dlya raspredeleniya chisel serii v sluchainoi posledovatelnosti, upravlyaemoi statsionarnoi tsepyu Markova”, PDM, 2017, no. 35, 14–28  mathnet  crossref
    2. N. M. Mezhennaya, “O predelnom raspredelenii chisla serii v polinomialnoi posledovatelnosti, upravlyaemoi tsepyu Markova”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 26:3 (2016), 324–335  mathnet  crossref  mathscinet  elib
    3. Corzo J.A., Vergara M.E., “A Data Driven Runs Test to Identify First Order Positive Markovian Dependence”, Hacet. J. Math. Stat., 45:2 (2016), 521–540  crossref  mathscinet  zmath  isi  scopus
    4. L. Ya. Savelev, S. V. Balakin, “Nekotorye primeneniya stokhasticheskoi teorii serii”, Sib. zhurn. industr. matem., 15:3 (2012), 111–123  mathnet  mathscinet
    5. L. Ya. Savelev, S. V. Balakin, “A stochastic model of a digit transfer by computing”, Num. Anal. Appl., 6:1 (2013), 71–76  mathnet  crossref  elib
    6. V. A. Barvinok, V. I. Bogdanovich, A. N. Plotnikov, “K voprosu o predelnom raspredelenii serii v sluchainoi dvoichnoi posledovatelnosti”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 4(29) (2012), 56–71  mathnet  crossref
    7. Kargapolova N.A., Ogorodnikov V.A., “Inhomogeneous Markov Chains with Periodic Matrices of Transition Probabilities and their Application to Simulation of Meteorological Processes”, Russ. J. Numer. Anal. Math. Model, 27:3 (2012), 213–228  crossref  mathscinet  zmath  isi  elib  scopus
    8. V. S. Lugavov, “On some class of functionals on transitions of Markov chain”, J. Math. Sci., 198:5 (2014), 580–601  mathnet  crossref
    9. L. Ya. Savelyev, S. V. Balakin, “A combinatorial approach to calculation of moments of characteristics of runs in ternary Markov sequences”, Discrete Math. Appl., 21:1 (2011), 47–67  mathnet  crossref  crossref  mathscinet  elib
    10. M. M. Lavrent'ev, L. Ja. Savel'ev, S. V. Balakin, “Special operator equations”, J. Appl. Industr. Math., 3:2 (2009), 246–258  mathnet  crossref  mathscinet
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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