Limit theorems for some branching measure-valued processes

Details Limit theorems for some branching measure-valued processes Limit theorems for some branching measure-valued processes

2011-06-03

arxiv.org/abs/1106.0660v2

Mathematics

Probability

Scientific paper

We consider a particles system in continuous time, discrete population, with spatial motion, and nonlocal branching. The offspring weights and their number may depend on the mother's weight. Our setting capture, for instance, the processes indexed by Galton-Watson tree. Using an (size-biased) auxiliary process for the empirical measure, we determine this asymptotic behaviour. Our model is a microscopic description of a random (discrete) population of individuals. We also obtain a large population approximation as weak solution of a growth-fragmentation equation. A size-structured population model and an infected cell model illustrate our results.

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