Electronic Journal of Probability

Stable continuous-state branching processes with immigration and Beta-Fleming-Viot processes with immigration

Clément Foucart and Olivier Hénard

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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.

Article information

Electron. J. Probab., Volume 18 (2013), paper no. 23, 21 pp.

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60J25 60G09 92D25

Measure-valued processes Continuous-state branching processes Fleming-Viot processes Immigration Beta-Coalescent Generators Random time change

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Foucart, Clément; Hénard, Olivier. Stable continuous-state branching processes with immigration and Beta-Fleming-Viot processes with immigration. Electron. J. Probab. 18 (2013), paper no. 23, 21 pp. doi:10.1214/EJP.v18-2024. https://projecteuclid.org/euclid.ejp/1465064248

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