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2013 Stable continuous-state branching processes with immigration and Beta-Fleming-Viot processes with immigration
Clément Foucart, Olivier Hénard
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Electron. J. Probab. 18: 1-21 (2013). DOI: 10.1214/EJP.v18-2024


Branching processes and Fleming-Viot processes are two main models in stochastic population theory. Incorporating an immigration in both models, we generalize the results of Shiga (1990) and Birkner (2005) which respectively connect the Feller diffusion with the classical Fleming-Viot process and the $\alpha$-stable continuous state branching process with the $Beta(2-\alpha,\alpha)$-generalized Fleming-Viot process. In a recent work, a new class of probability-measure valued processes, called $M$-generalized Fleming-Viot processes with immigration, has been set up in duality with the so-called $M$ coalescents. The purpose of this article is to investigate the links between this new class of processes and the continuous-state branching processes with immigration. In the specific case of the $\alpha$-stable branching process conditioned to be never extinct, we get that its genealogy is given, up to a random time change, by a $Beta(2-\alpha, \alpha-1)$-coalescent.


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Clément Foucart. Olivier Hénard. "Stable continuous-state branching processes with immigration and Beta-Fleming-Viot processes with immigration." Electron. J. Probab. 18 1 - 21, 2013.


Accepted: 12 February 2013; Published: 2013
First available in Project Euclid: 4 June 2016

zbMATH: 06247192
MathSciNet: MR3035751
Digital Object Identifier: 10.1214/EJP.v18-2024

Primary: 60J25 60G09 92D25

Keywords: beta-coalescent , continuous-state branching processes , Fleming-Viot processes , generators , immigration , Measure-valued processes , Random time change


Vol.18 • 2013
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