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Limites en grande population du modèle de Moran et chaines de Markov bifurcantes

Abstract : This thesis jointly supervised by Clermont Auvergne University and Assane Seck University in Ziguinchor constitutes a scientific study based on two population models: the Moran model and the bifurcating Markov chains. Each of them is a main research topic. Their richness is of extraordinary quality through their diversity and the aspects they abound. For the Moran model, we study a quantification of the error made by approximating the discrete Moran process by a Wright-Fisher diffusion. This quantification is done in the presence of weak immigration and weak selection. Under the effect of environmental aspects, we have an exponential control in time of the error. By comparing the selection and immigration parameters, linear and time-uniform controls are obtained. For more details, you can refer to articles (1) and (2) which are in the second part of this manuscript.For the second point of this thesis, we are interested in bifurcating Markov chains. More precisely to the principles of moderate deviations for bounded functionals and dependent on a variable. This has been the subject of an article (Article 3) which is found in the second part of this manuscript.Further more detailed studies are near to complete those found in this manuscript.
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Submitted on : Tuesday, May 10, 2022 - 10:36:29 AM
Last modification on : Wednesday, May 11, 2022 - 3:48:25 AM


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  • HAL Id : tel-03663404, version 1


Gorgui Gackou. Limites en grande population du modèle de Moran et chaines de Markov bifurcantes. Statistiques [math.ST]. Université Clermont Auvergne; Université Assane Seck (Ziguinchor, Sénégal), 2021. Français. ⟨NNT : 2021UCFAC080⟩. ⟨tel-03663404⟩



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