COX, Alexander; HORTON, E; VILLEMONAIS, D

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COX, Alexander
University of Bath [Bath]

HORTON, E
Méthodes avancées d’apprentissage statistique et de contrôle [ASTRAL]

VILLEMONAIS, D
Biology, genetics and statistics [BIGS]
Institut Élie Cartan de Lorraine [IECL]

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Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques. 2024

Institut Henri Poincaré (IHP)

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2024

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The aim of this paper is to study the large population limit of a binary branching particle system with Moran type interactions: we introduce a new model where particles evolve, reproduce and die independently and, with a probability that may depend on the configuration of the whole system, the death of a particle may trigger the reproduction of another particle, while a branching event may trigger the death of an other one. We study the occupation measure of the new model, explicitly relating it to the Feynman-Kac semigroup of the underlying Markov evolution and quantifying the L 2 distance between their normalisations. This model extends the fixed size Moran type interacting particle system discussed in [18, 19, 6, 7, 57] and we will indeed show that our model outperforms the latter when used to approximate a birth and death process. We discuss several other applications of our model including the neutron transport equation [36, 15] and population size dynamics.< Leer menos

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interacting particle systems

branching processes

many-to-one

Markov processes

birth-and-death process

Moran model

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Binary branching processes with Moran type interactions

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