Catalytic branching processes via spine techniques and renewal theory

Leif Doering (1) , Matthew Roberts (1)

1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires

In this article we contribute to the moment analysis of branching processes in catalytic media. The many-to-few lemma based on the spine technique is used to derive a system of (discrete space) partial differential equations for the number of particles in a variation of constants formulation. The long-time behavior is then deduced from renewal theorems and induction.

Domaines: Probabilités [math.PR]

Leif Doering, Matthew Roberts. Catalytic branching processes via spine techniques and renewal theory. 2011. ⟨hal-00605898⟩