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Functional Limit Theorems for the Pólya Urn

Author

Listed:
  • Dimitris Cheliotis

    (National and Kapodistrian University of Athens)

  • Dimitra Kouloumpou

    (Hellenic Naval Academy)

Abstract

For the plain Pólya urn with two colors, black and white, we prove a functional central limit theorem for the number of white balls, assuming that the initial number of black balls is large. Depending on the initial number of white balls, the limit is either a pure birth process or a diffusion.

Suggested Citation

  • Dimitris Cheliotis & Dimitra Kouloumpou, 2022. "Functional Limit Theorems for the Pólya Urn," Journal of Theoretical Probability, Springer, vol. 35(3), pages 2038-2051, September.
    • Handle: RePEc:spr:jotpro:v:35:y:2022:i:3:d:10.1007_s10959-021-01123-3
    DOI: 10.1007/s10959-021-01123-3
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    References listed on IDEAS

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    1. Janson, Svante, 2004. "Functional limit theorems for multitype branching processes and generalized Pólya urns," Stochastic Processes and their Applications, Elsevier, vol. 110(2), pages 177-245, April.
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