Binary branching processes with Moran type interactions
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 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 L2 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.
Cite
@article{arxiv.2207.03323,
title = {Binary branching processes with Moran type interactions},
author = {Alexander M. G. Cox and Emma Horton and Denis Villemonais},
journal= {arXiv preprint arXiv:2207.03323},
year = {2024}
}