Functional Limit Theorems for the Pólya Urn

Dimitris Cheliotis () and Dimitra Kouloumpou ()
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Dimitris Cheliotis: National and Kapodistrian University of Athens
Dimitra Kouloumpou: Hellenic Naval Academy

Journal of Theoretical Probability, 2022, vol. 35, issue 3, 2038-2051

Abstract: 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.

Keywords: Pólya urn; Functional limit theorems; Birth processes; Diffusion processes; 60F17; 60K99; 60C05 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10959-021-01123-3

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