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

Author

Listed:
  • Giacomo Aletti

    (Environmental Science and Policy Department, Università degli Studi di Milano, 20133 Milan, Italy
    These authors contributed equally to this work.)

  • Irene Crimaldi

    (IMT School for Advanced Studies Lucca, 55100 Lucca, Italy
    These authors contributed equally to this work.)

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.

Suggested Citation

  • Giacomo Aletti & Irene Crimaldi, 2021. "The Rescaled Pólya Urn and the Wright—Fisher Process with Mutation," Mathematics, MDPI, vol. 9(22), pages 1-11, November.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:22:p:2909-:d:679773
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    References listed on IDEAS

    as
    1. Giacomo Aletti & Irene Crimaldi & Fabio Saracco, 2021. "A model for the Twitter sentiment curve," PLOS ONE, Public Library of Science, vol. 16(4), pages 1-28, April.
    2. Gourieroux, Christian & Jasiak, Joann, 2006. "Multivariate Jacobi process with application to smooth transitions," Journal of Econometrics, Elsevier, vol. 131(1-2), pages 475-505.
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