Alpha-stable branching and beta-coalescents
- Publikationstyp:
- Zeitschriftenaufsatz
- Metadaten:
-
- Autoren
- Matthias Birkner
- Jochen Blath
- Marcella Capaldo
- Alison Etheridge
- Martin Möhle
- Jason Schweinsberg
- Anton Wakolbinger
- DOI
- 10.1214/ejp.v10-241
- ISSN
- 1083-6489
- Ausgabe der Veröffentlichung
- none
- Zeitschrift
- Electronic Journal of Probability
- Datum der Veröffentlichung
- 2005
- Status
- Published
- Herausgeber
- Institute of Mathematical Statistics
- Herausgeber URL
- http://dx.doi.org/10.1214/ejp.v10-241
- Datum der Datenerfassung
- 2021
- Titel
- Alpha-Stable Branching and Beta-Coalescents
- Ausgabe der Zeitschrift
- 10
Datenquelle: Crossref
- Andere Metadatenquellen:
-
- Abstract
- 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-distibution 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 spririt 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.
- Autoren
- M Birkner
- J Blath
- M Capaldo
- A Etheridge
- M Mohle
- J Schweinsberg
- A Wakolbinger
- DOI
- 10.1214/EJP.v10-241
- ISSN
- 1083-6489
- Zeitschrift
- ELECTRONIC JOURNAL OF PROBABILITY
- Notes
- article-number: 9 orcid-numbers: Etheridge, Alison/0000-0003-3669-8423 unique-id: WOS:000227484900004
- Paginierung
- 303 - 325
- Datum der Veröffentlichung
- 2005
- Datum der Datenerfassung
- 2022
- Titel
- Alpha-stable branching and beta-coalescents
- Sub types
- article
- Ausgabe der Zeitschrift
- 10
Datenquelle: Manual
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