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2013 | OriginalPaper | Chapter

Catalytic Branching Processes via Spine Techniques and Renewal Theory

Authors : Leif Döring, Matthew I. Roberts

Published in: Séminaire de Probabilités XLV

Publisher: Springer International Publishing

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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.

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previous chapter An Elementary Proof that the First Hitting Time of an Open Set by a Jump Process is a Stopping Time

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Title: Catalytic Branching Processes via Spine Techniques and Renewal Theory
Authors: Leif Döring
Matthew I. Roberts
Publisher: Springer International Publishing
Book: Séminaire de Probabilités XLV
Print ISBN: 978-3-319-00320-7

Electronic ISBN: 978-3-319-00321-4

Copyright Year: 2013
DOI: https://doi.org/10.1007/978-3-319-00321-4_12