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.
Keywords
- Finite Variance
- Moment Analysis
- Renewal Theory
- Offspring Distribution
- Renewal Theorem
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Acknowledgements
Leif Döring would like to thank Martin Kolb for drawing his attention to [1] and Andreas Kyprianou for his invitation to the Bath-Paris workshop on branching processes, where he learnt of the many-to-few lemma from Matthew I. Roberts. The authors would also like to thank Piotr Milos for checking an earlier draft, and a referee for pointing out several relevant articles.Leif Döring acknowledges the support of the Fondation Sciences Mathématiques de Paris. Matthew I. Roberts thanks ANR MADCOF (grant ANR-08-BLAN-0220-01) and WIAS for their support.
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Döring, L., Roberts, M.I. (2013). Catalytic Branching Processes via Spine Techniques and Renewal Theory. In: Donati-Martin, C., Lejay, A., Rouault, A. (eds) Séminaire de Probabilités XLV. Lecture Notes in Mathematics(), vol 2078. Springer, Heidelberg. https://doi.org/10.1007/978-3-319-00321-4_12
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