Catalytic branching processes via spine techniques and renewal theory

Abstract

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 behaviour is then deduced from renewal theorems and induction.

13 pages, 1 figure. Update: corrections and alterations throughout

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