Etienne Pardoux - Continuous branching processes : the discrete hidden in the continuous

arima:1899 - Revue Africaine de la Recherche en Informatique et Mathématiques Appliquées, November 25, 2008, Volume 9, 2007 Conference in Honor of Claude Lobry, 2008 - https://doi.org/10.46298/arima.1899
Continuous branching processes : the discrete hidden in the continuous

Authors: Etienne Pardoux

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.


Volume: Volume 9, 2007 Conference in Honor of Claude Lobry, 2008
Published on: November 25, 2008
Submitted on: May 6, 2008
Keywords: Continuous branching, Immortal individuals, Bienaymé–Galton–Watson processes, Lévy processes, Feller diffusion,Branchement continu,Individus à progéniture immortelle,Processus de Bienaymé– Galton–Watson,Processus de Lévy,Diffusion de Feller,[INFO] Computer Science [cs],[MATH] Mathematics [math]


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