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A Markov chain with number-theoretic limit distribution

  • Andrey M. Zubkov EMAIL logo und Kseniya A. Kolesnikova
Veröffentlicht/Copyright: 26. April 2016
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Abstract

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.


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


Award Identifier / Grant number: 14-50-00005

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

References

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Received: 2015-4-17
Published Online: 2016-4-26
Published in Print: 2016-4-1

2016 Walter de Gruyter GmbH, Berlin/Boston

Heruntergeladen am 30.11.2025 von https://www.degruyterbrill.com/document/doi/10.1515/dma-2016-0010/pdf?lang=de
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