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The characterization of tenable Pólya urns

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  • Davidson, Allison
  • D. Ward, Mark

Abstract

We characterize tenable Pólya urn schemes via a decomposition of their replacement matrices into small submatrices with certain conditions on the determinants. The characterization also involves an interplay between the submatrices and the initial conditions, as well as certain divisibility conditions.

Suggested Citation

  • Davidson, Allison & D. Ward, Mark, 2018. "The characterization of tenable Pólya urns," Statistics & Probability Letters, Elsevier, vol. 135(C), pages 38-43.
    • Handle: RePEc:eee:stapro:v:135:y:2018:i:c:p:38-43
    DOI: 10.1016/j.spl.2017.11.013
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    References listed on IDEAS

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    1. Bai, Z. D. & Hu, Feifang, 1999. "Asymptotic theorems for urn models with nonhomogeneous generating matrices," Stochastic Processes and their Applications, Elsevier, vol. 80(1), pages 87-101, March.
    2. Gouet, Raúl, 1989. "A martingale approach to strong convergence in a generalized Pólya-Eggenberger urn model," Statistics & Probability Letters, Elsevier, vol. 8(3), pages 225-228, August.
    3. Hajime Yamato, 1993. "A pólya urn model with a continuum of colors," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 45(3), pages 453-458, September.
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