| Título: | Alpha-Stable Branching and Beta-Coalescents |
| Autores: |
Birkner, Matthias; Weierstrass Institute for Applied Analysis and Stochastics, Germany Blath, Jochen; University of Oxford, UK Capaldo, Marcella; University of Oxford, UK Etheridge, Alison M.; University of Oxford, UK Möhle, Martin; University of Tübingen, Germany Schweinsberg, Jason; University of California at San Diego, USA Wakolbinger, Anton; J. W. Goethe Universität |
| Fecha: | 2005-01-01 |
| Publicador: | Electronic journal of probability |
| Fuente: |
 |
| Tipo: |
Peer-reviewed Article |
| Tema: | No aplica |
| Descripción: | We determine that the continuous-state branching processes for which the genealogy, suitably time-changed, can be described by an autonomous Markov process are precisely those arising from $\alpha$-stable branching mechanisms. The random ancestral partition is then a time-changed $\Lambda$-coalescent, where $\Lambda$ is the Beta-distribution with parameters $2-\alpha$ and $\alpha$, and the time change is given by $Z^{1-\alpha}$, where $Z$ is the total population size. For $\alpha = 2$ (Feller's branching diffusion) and $\Lambda = \delta_0$ (Kingman's coalescent), this is in the spirit of (a non-spatial version of) Perkins' Disintegration Theorem. For $\alpha =1$ and $\Lambda$ the uniform distribution on $[0,1]$, this is the duality discovered by Bertoin & Le Gall (2000) between the norming of Neveu's continuous state branching process and the Bolthausen-Sznitman coalescent. We present two approaches: one, exploiting the `modified lookdown construction', draws heavily on Donnelly & Kurtz (1999); the other is based on direct calculations with generators. |
| Idioma: | No aplica |
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