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

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 pred...

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Autores principales:	Giacomo Aletti, Irene Crimaldi
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	Pólya urn predictive mean urn model Wright—Fisher diffusion Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/9c59a411d040471eb47fbc05a11bc6c9
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spelling	oai:doaj.org-article:9c59a411d040471eb47fbc05a11bc6c92021-11-25T18:17:07ZThe Rescaled Pólya Urn and the Wright—Fisher Process with Mutation10.3390/math92229092227-7390https://doaj.org/article/9c59a411d040471eb47fbc05a11bc6c92021-11-01T00:00:00Zhttps://www.mdpi.com/2227-7390/9/22/2909https://doaj.org/toc/2227-7390In 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.Giacomo AlettiIrene CrimaldiMDPI AGarticlePólya urnpredictive meanurn modelWright—Fisher diffusionMathematicsQA1-939ENMathematics, Vol 9, Iss 2909, p 2909 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Pólya urn predictive mean urn model Wright—Fisher diffusion Mathematics QA1-939
spellingShingle	Pólya urn predictive mean urn model Wright—Fisher diffusion Mathematics QA1-939 Giacomo Aletti Irene Crimaldi The Rescaled Pólya Urn and the Wright—Fisher Process with Mutation
description	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.
format	article
author	Giacomo Aletti Irene Crimaldi
author_facet	Giacomo Aletti Irene Crimaldi
author_sort	Giacomo Aletti
title	The Rescaled Pólya Urn and the Wright—Fisher Process with Mutation
title_short	The Rescaled Pólya Urn and the Wright—Fisher Process with Mutation
title_full	The Rescaled Pólya Urn and the Wright—Fisher Process with Mutation
title_fullStr	The Rescaled Pólya Urn and the Wright—Fisher Process with Mutation
title_full_unstemmed	The Rescaled Pólya Urn and the Wright—Fisher Process with Mutation
title_sort	rescaled pólya urn and the wright—fisher process with mutation
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/9c59a411d040471eb47fbc05a11bc6c9
work_keys_str_mv	AT giacomoaletti therescaledpolyaurnandthewrightfisherprocesswithmutation AT irenecrimaldi therescaledpolyaurnandthewrightfisherprocesswithmutation AT giacomoaletti rescaledpolyaurnandthewrightfisherprocesswithmutation AT irenecrimaldi rescaledpolyaurnandthewrightfisherprocesswithmutation
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The Rescaled Pólya Urn and the Wright—Fisher Process with Mutation

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