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Abstract
AbstractWe 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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Grigorescu I, Kang M. Critical Scale for a Continuous AIMD Model. STOCH MODELS 2014. [DOI: 10.1080/15326349.2014.932697] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
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Balázs M, Rácz MZ, Tóth B. Modeling flocks and prices: Jumping particles with an attractive interaction. ANNALES DE L'INSTITUT HENRI POINCARÉ, PROBABILITÉS ET STATISTIQUES 2014. [DOI: 10.1214/12-aihp512] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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