# Genealogy of flows of continuous-state branching processes via flows of partitions and the Eve property

Abstract : We encode the genealogy of a continuous-state branching process associated with a branching mechanism $\Psi$ - or $\Psi$-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 $\Psi$-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.
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Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques, Institute Henri Poincaré, 2014, 50 (3), pp.732 - 769
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https://hal.archives-ouvertes.fr/hal-00694393
Contributeur : Cyril Labbé <>
Soumis le : vendredi 4 mai 2012 - 10:50:58
Dernière modification le : dimanche 8 janvier 2017 - 01:04:04

### Identifiants

• HAL Id : hal-00694393, version 1
• ARXIV : 1205.0764

### Citation

Cyril Labbé. Genealogy of flows of continuous-state branching processes via flows of partitions and the Eve property. Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques, Institute Henri Poincaré, 2014, 50 (3), pp.732 - 769. <hal-00694393>

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