WIAS Preprint No. 1626, (2011)

Catalytic branching processes via spine techniques and renewal theory



Authors

  • Döring, Leif
  • Roberts, Matthew I.

2010 Mathematics Subject Classification

  • 60J27 60J80

Keywords

  • Catalytic branching process, moments, renewal theory, many-to-few, spine

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 behavior is then deduced from renewal theorems and induction.

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