The Rescaled Pólya Urn and the Wright—Fisher Process with Mutation

Giacomo Aletti and Irene Crimaldi
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Giacomo Aletti: Environmental Science and Policy Department, Università degli Studi di Milano, 20133 Milan, Italy
Irene Crimaldi: IMT School for Advanced Studies Lucca, 55100 Lucca, Italy

Mathematics, 2021, vol. 9, issue 22, 1-11

Abstract: In recent papers the authors introduce, study and apply a variant of the Eggenberger—Pólya urn, called the “rescaled” Pólya urn, which, for a suitable choice of the model parameters, exhibits a reinforcement mechanism mainly based on the last observations, a random persistent fluctuation of the predictive mean and the almost sure convergence of the empirical mean to a deterministic limit. In this work, motivated by some empirical evidence, we show that the multidimensional Wright—Fisher diffusion with mutation can be obtained as a suitable limit of the predictive means associated to a family of rescaled Pólya urns.

Keywords: Pólya urn; predictive mean; urn model; Wright—Fisher diffusion (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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