Évènement

Ibrahima Drame
I2M, Aix-Marseille université

Date(s) : 22/05/2017   iCal
13h30 - 15h30

In this thesis, we study the convergence of the exploration process of the non-binary tree associated to a continuous time branching process, in the limit of a large population. In the first part, we give a precise description of the exploration process of the non-binary tree. We then describe a bijection between exploration processes and Galton Watson non-binary trees. After some renormalization, we present the results of convergence of the population process and the exploration process, in the limit of a large populations.In the second part, we first establish the convergence of the population process to a continuous state branching process (CSBP) with jumps. We then show the convergence of the (rescaled) exploration process, of the corresponding genealogical tree towards the continuous height process recently defined by Li, Pardoux and Wakolbinger. In the last part, we consider a population model with interaction defined with a more general non linear function. We proceed to a renormalization of the parameters model and we obtain in limit a generalized CSBP. We then renormalize the height process of the associated genealogical tree, and take the weak limit as the size of the population tends to infinity.

*Membres du jury :

– Vincent BANSAYE, Ecole Polytechnique de Paris, Rapporteur
– Romain ABRAHAM, Université d’Orléans, Examinateur
– Ahmadou Bamba SOW, Université Gaston Berger du Sénégal, Codirecteur
– Etienne PARDOUX, Aix-Marseille Universite, Directeur
– Thomas DUQUESNE, Université Pierre et Marie Curie, Rapporteur
– Anton WAKOLBINGER, J. W. Goethe Universitat, Germany, Examinateur

Liens :
– Université Gaston Berger – Saint-Louis du Sénégal (cotutelle)
– theses.fr

Catégories

• Soutenance de thèse