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- W2170708932 abstract "Feller diffusion is a continuous branching process. The branching property tells us that for t > 0 fixed, when indexed by the initial condition, it is a subordinator (i. e. a positive-valued Levy process), which is fact is a compound Poisson process. The number of points of this Poisson process can be interpreted as the number of individuals whose progeny survives during a number of generations of the order of t ◊ N, where N denotes the size of the population, in the limit N ! 1. This fact follows from recent results of Bertoin, Fontbona, Martinez (1). We compare them with older results of de O'Connell (7) and (8). We believe that this comparison is useful for better understanding these results. There is no new result in this presentation. RESUME. La diffusion de Feller est un processus de branchement continu. La propriete de bran- chement nous dit que a t > 0 fixe, indexe par la condition initiale, ce processus est un subordinateur (processus de Levy a valeurs positives), qui est en fait un processus de Poisson compose. Le nombre de points de ce processus de Poisson s'interprete comme le nombre d'individus dont la descendance survit au cours d'un nombre de generations de l'ordre de t ◊ N, ou N designe la taille de la popu- lation, dans la limite N ! 1. Ce fait decoule de resultats recents de Bertoin, Fontbona, Martinez (1). Nous le rapprochons de resultats plus anciens de O'Connell (7) et (8). Ce rapprochement nous semble aider a mieux comprendre ces resultats. Cet article ne contient pas de resultat nouveau." @default.
- W2170708932 created "2016-06-24" @default.
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- W2170708932 date "2008-01-01" @default.
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- W2170708932 title "Continuous branching processes : the discrete hidden in the continuous" @default.
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