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


 
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1. Title Title of document Stable continuous-state branching processes with immigration and Beta-Fleming-Viot processes with immigration
 
2. Creator Author's name, affiliation, country Clément Foucart; Université Pierre et Marie Curie Paris 6; France
 
2. Creator Author's name, affiliation, country Olivier Hénard; École des Ponts, Université Paris-Est; France
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Measure-valued processes, Continuous-state branching processes, Fleming-Viot processes, Immigration, Beta-Coalescent, Generators, Random time change
 
3. Subject Subject classification 60J25 60G09 92D25
 
4. Description Abstract 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.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) ANR-08-BLAN-0190
 
7. Date (YYYY-MM-DD) 2013-02-12
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/2024
 
10. Identifier Digital Object Identifier 10.1214/EJP.v18-2024
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 18
 
12. Language English=en en
 
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