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Limit theorems for some branching measure-valued processes

  • Bertrand Cloez (a1)


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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* Postal address: INRA Montpellier, UMR MISTEA, Bâtiment 29, 2 Place Pierre Viala, 34060 Montpellier Cedex 1, France. Email address:


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Limit theorems for some branching measure-valued processes

  • Bertrand Cloez (a1)


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