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

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

2009-08-26

arxiv.org/abs/0908.3735v2

Mathematics

Probability

Published in Annals of Applied Probability vol. 20, n. 6 (2010) pp. 1967-1988

Scientific paper

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.

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