2022/07/07 by Alexander M. G. Cox, Cox, Alexander M. G., E Horton +3
Business, Management and Accounting · Mathematics · Physics and Astronomy · #Advanced Queuing Theory Analysis #FOS: Mathematics #Probability (math.PR) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.2207.03323
openalex publication_date 2022/07/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.