Binary branching processes with Moran type interactions
Language
en
Article de revue
This item was published in
Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques. 2024
Institut Henri Poincaré (IHP)
Date
2024English Abstract
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 ...Read more >
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.Read less <
English Keywords
interacting particle systems
branching processes
many-to-one
Markov processes
birth-and-death process
Moran model
Origin
Hal imported