Alexander Cox (University of Bath)

“Binary branching processes with Moran type interactions”

Abstract. In this talk, we will discuss 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 another 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 Del Moral, Burdzy et al, and Villemonais, 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, Sequential Monte Carlo methods, and population size dynamics.

Joint work with Emma Horton and Denis Villemonais.