On the Eve property for CSBP

Thomas Duquesne (1) , Cyril Labbé (1)

1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires

We consider the population model associated to continuous state branching processes and we are interested in the so-called Eve property that asserts the existence of an ancestor with an overwhelming progeny at large times, and more generally, in the possible behaviours of the frequencies among the population at large times. In this paper, we classify all the possible behaviours according to the branching mechanism of the continuous state branching process.

Mots clés: Continuous state branching process; Eve; dust; Grey martingale; frequency distribution

Domaines: Probabilités [math.PR]

Thomas Duquesne, Cyril Labbé. On the Eve property for CSBP. Electronic Journal of Probability, 2014, 19 (6), pp.1-31. ⟨10.1214/EJP.v19-2831⟩. ⟨hal-00826898v2⟩