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

Soumaya Idriss and Hosam Mahmoud ()
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Soumaya Idriss: Monastir University
Hosam Mahmoud: The George Washington University

Methodology and Computing in Applied Probability, 2023, vol. 25, issue 2, 1-16

Abstract: 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.

Keywords: Pólya urn; Dynamic urn; $$L^2$$ L 2 -limit theorems; Symbolic manipulation; Asymptotic; Primary: 60C05; 60F25 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s11009-023-10034-1

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