Asymptotic regimes for the partition into colonies of a branching process with emigration

Jean Bertoin (1, 2)

1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires
2 DMA - Département de Mathématiques et Applications - ENS Paris

We consider a spatial branching process with emigration in which children either remain at the same site as their parents or migrate to new locations and then found their own colonies. We are interested in asymptotics of the partition of the total population into colonies for large populations with rare migrations. Under appropriate regimes, we establish weak convergence of the rescaled partition to some random measure that is constructed from the restriction of a Poisson point measure to a certain random region, and whose cumulant solves a simple integral equation.

Mots clés: Branching process; emigration; random partition; cumulant; weak convergence

Domaines: Probabilités [math.PR]

Jean Bertoin. Asymptotic regimes for the partition into colonies of a branching process with emigration. 2010. ⟨hal-00411081v2⟩