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Teor. Veroyatnost. i Primenen., 1974, Volume 19, Issue 1, Pages 182–187 (Mi tvp2773)  

This article is cited in 7 scientific papers (total in 7 papers)

Short Communications

Limit distributions of random variables connected with multiple long duplications in a sequence lof independent trials

V. G. Mikhailov

Moscow

Abstract: Let $X_0,X_1,…$ be a sequence of independent trials with $m$ outcomes. We prove limit theorems for the distribution of the number of multiple long duplications
\begin{gather*} ((X_{i_1}, X_{i_1+1},…,X_{i_1+n-1})=(X_{i_t}, X_{i_t+1},…,X_{i_t+n-1})
t=2,…,k,\quad1\le i_1<…<i_k\le N), \end{gather*}
for the distribution of the waiting time until the first multiple duplication of a given length and for the distribution of the maximal duplication length.

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English version:
Theory of Probability and its Applications, 1974, 19:1, 180–184

Bibliographic databases:

Document Type: Article
Received: 01.10.1973

Citation: V. G. Mikhailov, “Limit distributions of random variables connected with multiple long duplications in a sequence lof independent trials”, Teor. Veroyatnost. i Primenen., 19:1 (1974), 182–187; Theory Probab. Appl., 19:1 (1974), 180–184

Citation in format AMSBIB
\Bibitem{Mik74}
\by V.~G.~Mikhailov
\paper Limit distributions of random variables connected with multiple long duplications in a~sequence lof independent trials
\jour Teor. Veroyatnost. i Primenen.
\yr 1974
\vol 19
\issue 1
\pages 182--187
\mathnet{http://mi.mathnet.ru/tvp2773}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=339310}
\zmath{https://zbmath.org/?q=an:0326.60025}
\transl
\jour Theory Probab. Appl.
\yr 1974
\vol 19
\issue 1
\pages 180--184
\crossref{https://doi.org/10.1137/1119018}


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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. V. G. Mikhailov, “Convergence to a process with independent increments in a scheme of increasing sums of dependent random variables”, Math. USSR-Sb., 23:2 (1974), 271–286  mathnet  crossref  mathscinet  zmath
    2. A. M. Shoitov, “Limit distributions of the number of sets of $H$-equivalent segments in an equiprobable polynomial scheme of arrays”, Discrete Math. Appl., 12:2 (2002), 165–181  mathnet  crossref  mathscinet  zmath
    3. 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
    4. V. A. Kopyttsev, V. G. Mikhailov, “An estimate of the approximation accuracy in B. A. Sevastyanov's limit theorem and its application in the problem of random inclusions”, Discrete Math. Appl., 25:3 (2015), 149–156  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    5. Vladimir G. Mikhaylov, “Estimates of accuracy of the Poisson approximation for the distribution of number of runs of long string repetitions in a Markov chain”, Discrete Math. Appl., 26:2 (2016), 105–113  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    6. V. G. Mikhailov, A. M. Shoitov, “Mnogokratnye povtoreniya dlinnykh tsepochek v konechnoi tsepi Markova”, Matem. vopr. kriptogr., 6:3 (2015), 117–133  mathnet  crossref  mathscinet  elib
    7. N. M. Mezhennaya, “O chisle sovpadenii znakov v diskretnoi sluchainoi posledovatelnosti, upravlyaemoi tsepyu Markova”, Sib. elektron. matem. izv., 13 (2016), 305–317  mathnet  crossref
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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