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The Mathematics of the Uncertain pp 421–429Cite as

Limit Behavior of Polya Urn Schemes

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Part of the book series: Studies in Systems, Decision and Control ((SSDC,volume 142))

Abstract

The long term behavior of the composition of Polya’s urn schemes is analyzed by means of simple martingale arguments. The results hold even under the assumption that random numbers of balls are added to the urn depending only on the color of the ball obtained in the successive extractions.

In memory of our colleague and friend Pedro Gil

Supported by Grant MTM 2016–75497-P, from the Spanish Ministerio de Economía y Competitividad.

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References

  1. Durret R (2010) Probability: theory and examples. Cambridge University Press, Cambridge

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  2. Johnson NL, Kotz S (1977) Urn models and their application. Wiley, New York

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  3. Kotz S, Balakrishnan N (1997) Advances in urn models during the past two decades. In: Balakrishnan N (ed) Advances in combinatorial methods and applications to probability and statistics. Birkhäuser, Boston

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  4. Mahmoud HM (2009) Polya urn models. Chapman and Hall/CRC, London

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  5. Feller W (1971) An introduction to probability theory and its applications, vol II. Wiley, New York

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  6. Flajolet P, Dumas P, Puyhaubert V (2006) Some exactly solvable models of urn process theory. In: DMTCS Proceedings, (Fourth colloquium on mathematics and computer science) AG:59–118

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Author information

Authors and Affiliations

  1. Department of Statistics–UNED, Senda del Rey, 9, 28040, Madrid, Spain

    Ricardo Vélez & Tomás Prieto-Rumeau

Authors
  1. Ricardo Vélez
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  2. Tomás Prieto-Rumeau
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Corresponding author

Correspondence to Ricardo Vélez .

Editor information

Editors and Affiliations

  1. Liberbank, Oviedo, Spain

    Eduardo Gil

  2. Viajes El Corte Inglés, Oviedo, Spain

    Eva Gil

  3. Funl Media, Oxford, United Kingdom

    Juan Gil

  4. Departamento de Estadística e Investigación Operativa y Didáctica de la Matemática, Facultad de Ciencias, Universidad de Oviedo, Oviedo, Spain

    María Ángeles Gil

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Vélez, R., Prieto-Rumeau, T. (2018). Limit Behavior of Polya Urn Schemes. In: Gil, E., Gil, E., Gil, J., Gil, M. (eds) The Mathematics of the Uncertain. Studies in Systems, Decision and Control, vol 142. Springer, Cham. https://doi.org/10.1007/978-3-319-73848-2_40

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  • DOI: https://doi.org/10.1007/978-3-319-73848-2_40

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-73847-5

  • Online ISBN: 978-3-319-73848-2

  • eBook Packages: EngineeringEngineering (R0)

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