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Diskr. Mat., 2015, Volume 27, Issue 3, Pages 17–24 (Mi dm1332)  

This article is cited in 1 scientific paper (total in 1 paper)

A Markov chain with number-theoretic limit distribution

Andrey M. Zubkov, Kseniya A. Kolesnikova

Steklov Mathematical Institute of RAS

Abstract: Let an urn contain balls of white and black colors. After each step with probabilities equal to $\frac12$ either the number of white balls is increased by the number of black balls or the number of black balls is increased by the number of white balls. Formulas for the first two moments of the total number of balls in an urn are derived and it is shown that the limiting distribution function of the proportion of the number of white balls in an urn coincides with the Minkowski number-theoretic function. \def\acknowledgementname{Funding

Keywords: discrete Markov chains, iterations of random mappings, limit distributions, Minkowski function

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/dm1332

Full text: PDF file (446 kB)
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English version:
Discrete Mathematics and Applications, 2016, 26:2, 125–130

Bibliographic databases:

Document Type: Article
UDC: 519.212.2+519.217.2
Received: 17.04.2015

Citation: Andrey M. Zubkov, Kseniya A. Kolesnikova, “A Markov chain with number-theoretic limit distribution”, Diskr. Mat., 27:3 (2015), 17–24; Discrete Math. Appl., 26:2 (2016), 125–130

Citation in format AMSBIB
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\yr 2015
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\pages 125--130
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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. A. M. Zubkov, K. A. Kolesnikova, “Limit theorem for the additive replacement process”, Theory Probab. Appl., 62:2 (2018), 319–327  mathnet  crossref  crossref  mathscinet  isi  elib
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