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Discrete Mathematics and Applications

Editor-in-Chief: Zubkov, Andrei

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CiteScore 2016: 0.16

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Volume 26, Issue 2


A Markov chain with number-theoretic limit distribution

Andrey M. Zubkov / Kseniya A. Kolesnikova
Published Online: 2016-04-26 | DOI: https://doi.org/10.1515/dma-2016-0010


Let an urn contain balls of white and black colors. After each step with probabilities equal to 12 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.

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

Originally published in Diskretnaya Matematika (2015) 27,.4, 17–24 (in Russian).


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About the article

Received: 2015-04-17

Published Online: 2016-04-26

Published in Print: 2016-04-01

Funding Source: Russian Science Foundation

Award identifier / Grant number: 14-50-00005

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

Citation Information: Discrete Mathematics and Applications, Volume 26, Issue 2, Pages 125–130, ISSN (Online) 1569-3929, ISSN (Print) 0924-9265, DOI: https://doi.org/10.1515/dma-2016-0010.

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Андрей Михайлович Зубков, Andrei Mikhailovich Zubkov, Ксения Алексеевна Колесникова, and Kseniya Alekseevna Kolesnikova
Теория вероятностей и ее применения, 2017, Volume 62, Number 2, Page 393

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