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A Markov chain with number-theoretic limit distribution

  • Andrey M. Zubkov EMAIL logo and Kseniya A. Kolesnikova
Published/Copyright: April 26, 2016
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Discrete Mathematics and Applications
From the journal Discrete Mathematics and Applications Volume 26 Issue 2

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.

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

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

Funding source: Russian Science Foundation

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

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https://doi.org/10.1515/dma-2016-0010
Keywords for this article
discrete Markov chains; iterations of random mappings; limit distributions; Minkowski function

Articles in the same Issue

  1. Frontmatter
  2. Article
  3. Functional limit theorems for the decomposable branching process with two types of particles
  4. Article
  5. Completeness problem for the class of linear automata functions
  6. Article
  7. Estimates of accuracy of the Poisson approximation for the distribution of number of runs of long string repetitions in a Markov chain
  8. Article
  9. Complexity of systems of functions of Boolean algebra and systems of functions of three-valued logic in classes of polarized polynomial forms
  10. Article
  11. A Markov chain with number-theoretic limit distribution
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