Catalytic branching processes via spine techniques and renewal theory
- Döring, Leif
- Roberts, Matthew I.
2010 Mathematics Subject Classification
- 60J27 60J80
- Catalytic branching process, moments, renewal theory, many-to-few, spine
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.