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Continuous branching processes : the discrete hidden in the continuous : Dedicated to Claude Lobry

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 Lévy 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 ―>µ. 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.
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Etienne Pardoux. Continuous branching processes : the discrete hidden in the continuous : Dedicated to Claude Lobry. Revue Africaine de la Recherche en Informatique et Mathématiques Appliquées, INRIA, 2008, Volume 9, 2007 Conference in Honor of Claude Lobry, 2008, pp.211-229. ⟨10.46298/arima.1899⟩. ⟨hal-01277832⟩

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