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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https://hal.archives-ouvertes.fr/hal-00694393
Contributor : Cyril Labbé <>
Submitted on : Friday, May 4, 2012 - 10:50:58 AM
Last modification on : Saturday, May 25, 2019 - 1:32:36 AM

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

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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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