REVERSAL PROPERTIES AND EXACT SIMULATION OF THE GENEALOGICAL TREE FOR A STATIONNARY BRANCHING POPULATIONReportar como inadecuado




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1 MAPMO - Mathématiques - Analyse, Probabilités, Modélisation - Orléans 2 CERMICS - Centre d-Enseignement et de Recherche en Mathématiques et Calcul Scientifique

Abstract : We consider a model of stationary population with random size given by a stationary continuous state branching process with a quadratic branching mechanism. We give an exact elementary simulation procedure of the genealogical tree of n individuals randomly chosen among the extant population at a given time. Then, we prove the convergence of the renormalized total length of this genealogical tree as n goes to infinity, see also Pfaffelhuber, Wakolbinger and Weisshaupt 2011 in the context of a constant size population. The proof is based on the ancestral process of the extant population at a fixed time which was defined by Aldous and Popovic 2005 in the critical case. We also present a reversal procedure on the genealogical tree of the whole population that consists in looking at the tree downward from its tip: the branching points becoming leaves and leaves becoming branching points. We prove that the distribution of the genealogical tree is invariant under this reversal procedure, which provides a better understanding of previous results from Bi and Delmas 2016.





Autor: Romain Abraham - Jean-François Delmas -

Fuente: https://hal.archives-ouvertes.fr/



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