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UID:1771@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20170522T133000
DTEND;TZID=Europe/Paris:20170522T153000
DTSTAMP:20241210T073106Z
URL:https://www.i2m.univ-amu.fr/evenements/processus-d-exploration-des-arb
 res-aleatoires-en-temps-continu-a-branchement-non-binaire-limite-en-grande
 -population/
SUMMARY:Ibrahima Drame (I2M\, Aix-Marseille université): Processus d'explo
 ration des arbres aléatoires en temps continu à branchement non binaire.
  Limite en grande population.
DESCRIPTION:Ibrahima Drame: In this thesis\, we study the convergence of th
 e exploration process of the non-binary tree associated to a continuous ti
 me branching process\, in the limit of a large population. In the first pa
 rt\, we give a precise description of the exploration process of the non-b
 inary tree. We then describe a bijection between exploration processes and
  Galton Watson non-binary trees. After some renormalization\, we present t
 he results of convergence of the population process and the exploration pr
 ocess\, 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 tow
 ards the continuous height process recently defined by Li\, Pardoux and Wa
 kolbinger. In the last part\, we consider a population model with interact
 ion defined with a more general non linear function. We proceed to a renor
 malization of the parameters model and we obtain in limit a generalized CS
 BP. We then renormalize the height process of the associated genealogical 
 tree\, and take the weak limit as the size of the population tends to infi
 nity.\n*Membres du jury :\n- Vincent BANSAYE\, Ecole Polytechnique de Pari
 s\, Rapporteur\n- Romain ABRAHAM\, Université d'Orléans\, Examinateur\n-
  Ahmadou Bamba SOW\, Université Gaston Berger du Sénégal\, Codirecteur\
 n- Etienne PARDOUX\, Aix-Marseille Universite\, Directeur\n- Thomas DUQUES
 NE\, Université Pierre et Marie Curie\, Rapporteur\n- Anton WAKOLBINGER\,
  J. W. Goethe Universitat\, Germany\, Examinateur\n\nLiens :\n- Universit
 é Gaston Berger - Saint-Louis du Sénégal (cotutelle)\n- theses.fr
CATEGORIES:Soutenance de thèse,ALEA,Probabilités
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