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Exact Covariances and Refined Asymptotics in Dichromatic Tenable Balanced Pólya Urn Schemes

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  • Soumaya Idriss

    (Monastir University)

  • Hosam Mahmoud

    (The George Washington University)

Abstract

In the present paper, we provide exact expressions and sharp asymptotics for the covariance matrix of a dichromatic time-dependent Pólyaurn. We follow a purely combinatorial approach. Although we take interest in the large-index case with a fixed replacement matrix (as it was left open in Mahmoud (2022)), the combinatorial approach we pursue also produces exact expressions and sharp asymptotics for both small- and critical-index urn schemes with fixed replacement matrices, as well as schemes with dynamic (time-dependent matrices). We provide examples elucidating each case, including two dynamic schemes.

Suggested Citation

  • Soumaya Idriss & Hosam Mahmoud, 2023. "Exact Covariances and Refined Asymptotics in Dichromatic Tenable Balanced Pólya Urn Schemes," Methodology and Computing in Applied Probability, Springer, vol. 25(2), pages 1-16, June.
    • Handle: RePEc:spr:metcap:v:25:y:2023:i:2:d:10.1007_s11009-023-10034-1
    DOI: 10.1007/s11009-023-10034-1
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    References listed on IDEAS

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    1. Zhang, Panpan & Chen, Chen & Mahmoud, Hosam, 2015. "Explicit characterization of moments of balanced triangular Pólya urns by an elementary approach," Statistics & Probability Letters, Elsevier, vol. 96(C), pages 149-153.
    2. 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.
    3. Smythe, R. T., 1996. "Central limit theorems for urn models," Stochastic Processes and their Applications, Elsevier, vol. 65(1), pages 115-137, December.
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