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Genealogy of flows of continuous-state branching processes via flows of partitions and the Eve property.
- Source :
-
Annales de l'Institut Henri Poincare (B) Probability & Statistics . Aug2014, Vol. 50 Issue 3, p732-769. 38p. - Publication Year :
- 2014
-
Abstract
- We encode the genealogy of a continuous-state branching process associated with a branching mechanism ψ - or ψ-CSBP in short - using a stochastic flow of partitions. This encoding holds for all branching mechanisms and appears as a very tractable object to deal with asymptotic behaviours and convergences. In particular we study the so-called Eve property - the existence of an ancestor from which the entire population descends asymptotically - and give a necessary and sufficient condition on the ψ-CSBP for this property to hold. Finally, we show that the flow of partitions unifies the lookdown representation and the flow of subordinators when the Eve property holds. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 02460203
- Volume :
- 50
- Issue :
- 3
- Database :
- Academic Search Index
- Journal :
- Annales de l'Institut Henri Poincare (B) Probability & Statistics
- Publication Type :
- Academic Journal
- Accession number :
- 97056106
- Full Text :
- https://doi.org/10.1214/13-AIHP542