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Diskr. Mat., 2015, Volume 27, Issue 4, Pages 67–78 (Mi dm1348)  

This article is cited in 9 scientific papers (total in 9 papers)

Estimates of accuracy of the Poisson approximation for the distribution of number of runs of long string repetitions in a Markov chain

Vladimir G. Mikhaylov

Steklov Mathematical Institute of RAS

Abstract: Let $X_0,X_1,\ldots$ be a simple ergodic Markov chain with a finite set of states and $\tilde\xi_{n,k}(s)$ be a number of runs of $k$-fold repetitions of strings having length $s$. Estimates of accuracy of the Poisson approximation for the distribution of $\xi_{n,k}(s)$ in the sequence $X_0,X_1,\ldots,X_{n+s-1}$ are obtained, these estimates are uniform over $k$. \def\acknowledgementname{Funding

Keywords: Markov chain, $k$-fold repetitions of $s$-strings, accuracy of the Poisson approximation.

Funding Agency Grant Number
Russian Science Foundation 14-50-00005
This work was supported by the Russian Science Foundation under grant no. 14-50-00005.


DOI: https://doi.org/10.4213/dm1348

Full text: PDF file (472 kB)
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English version:
Discrete Mathematics and Applications, 2016, 26:2, 105–113

Bibliographic databases:

UDC: 519.212.2
Received: 30.10.2015

Citation: 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”, Diskr. Mat., 27:4 (2015), 67–78; Discrete Math. Appl., 26:2 (2016), 105–113

Citation in format AMSBIB
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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. N. M. Mezhennaya, “O chisle sovpadenii znakov v diskretnoi sluchainoi posledovatelnosti, upravlyaemoi tsepyu Markova”, Sib. elektron. matem. izv., 13 (2016), 305–317  mathnet  crossref
    2. V. G. Mikhailov, “On the probability of existence of substrings with the same structure in a random sequence”, Discrete Math. Appl., 27:6 (2017), 377–386  mathnet  crossref  crossref  mathscinet  isi  elib
    3. N. M. Mezhennaya, “Otsenka dlya raspredeleniya chisel serii v sluchainoi posledovatelnosti, upravlyaemoi statsionarnoi tsepyu Markova”, PDM, 2017, no. 35, 14–28  mathnet  crossref
    4. A. M. Zubkov, O. P. Orlov, “Limit distributions of extremal distances to the nearest neighbor”, Discrete Math. Appl., 28:3 (2018), 189–199  mathnet  crossref  crossref  mathscinet  isi  elib
    5. V. G. Mikhailov, “On the reduction property of the number of $H$-equivalent tuples of states in a discrete Markov chain”, Discrete Math. Appl., 28:2 (2018), 75–82  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    6. V. I. Kruglov, “On coincidences of tuples in a $q$-ary tree with random labels of vertices”, Discrete Math. Appl., 28:5 (2018), 293–307  mathnet  crossref  crossref  mathscinet  isi  elib
    7. V. G. Mikhailov, N. M. Mezhennaya, “Normal approximation for $U$- and $V$-statistics of a stationary absolutely regular sequence”, Sib. elektron. matem. izv., 17 (2020), 672–682  mathnet  crossref
    8. I V. Masol , V S. Popereshnyak, “Checking the randomness of bits disposition in local segments of the (0,1)-sequence”, Cybern. Syst. Anal., 56:3 (2020), 513–520  crossref  mathscinet  zmath  isi
    9. V. G. Mikhailov, N. M. Mezhennaya, A. V. Volgin, “Ob usloviyakh asimptoticheskoi normalnosti chisla povtorenii v statsionarnoi sluchainoi posledovatelnosti”, Diskret. matem., 33:3 (2021), 64–78  mathnet  crossref
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