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Limit theorems for some branching measure-valued processes

Abstract : We consider a particle system in continuous time, a discrete population, with spatial motion, and nonlocal branching. The offspring's positions and their number may depend on the mother's position. Our setting captures, for instance, the processes indexed by a Galton-Watson tree. Using a size-biased auxiliary process for the empirical measure, we determine the asymptotic behaviour of the particle system. We also obtain a large population approximation as a weak solution of a growth-fragmentation equation. Several examples illustrate our results. The main one describes the behaviour of a mitosis model; the population is size structured. In this example, the sizes of the cells grow linearly and if a cell dies then it divides into two descendants.
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Bertrand Cloez. Limit theorems for some branching measure-valued processes. Advances in Applied Probability, Applied Probability Trust, 2017, 49 (2), pp.549-580. ⟨10.1017/apr.2017.12⟩. ⟨hal-01608460⟩

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