Limit theorems for some branching measure-valued processes

By Bertrand Cloez. Advances in Applied Probability, 2011

54 citations recorded by the source corpus.

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.

Subfields: Finance, Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/7256b9de8c33a35f852d28228717875f8e2c739d

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In Finance

1. Vincent Bansaye
2. Pierre Gabriel
3. Aline Marguet
4. Bertrand Cloez
5. Jinghai Shao

In Mathematical Physics

1. Bertrand Cloez
2. Vincent Bansaye
3. Aline Marguet
4. Pierre Gabriel

In Statistics and Probability

1. Vincent Bansaye
2. Pierre Gabriel
3. Bertrand Cloez
4. Aline Marguet
5. Jinghai Shao

Citations in the corpus

• A non‐conservative Harris ergodic theorem (2019, background): “These semigroups appear in particular for the study of branching processes [16, 27, 71] and large deviations [47, 63, 64].”