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1996 Multiple Space-Time Scale Analysis For Interacting Branching Models
Donald Dawson, Andreas Greven
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Electron. J. Probab. 1: 1-84 (1996). DOI: 10.1214/EJP.v1-14


We study a class of systems of countably many linearly interacting diffusions whose components take values in $[0, \inf)$ and which in particular includes the case of interacting (via migration) systems of Feller's continuous state branching diffusions. The components are labelled by a hierarchical group. The longterm behaviour of this system is analysed by considering space-time renormalised systems in a combination of slow and fast time scales and in the limit as an interaction parameter goes to infinity. This leads to a new perspective on the large scale behaviour (in space and time) of critical branching systems in both the persistent and non-persistent cases and including that of the associated historical process. Furthermore we obtain an example for a rigorous renormalization analysis.


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Donald Dawson. Andreas Greven. "Multiple Space-Time Scale Analysis For Interacting Branching Models." Electron. J. Probab. 1 1 - 84, 1996.


Accepted: 28 February 1996; Published: 1996
First available in Project Euclid: 25 January 2016

zbMATH: 0890.60093
MathSciNet: MR1423467
Digital Object Identifier: 10.1214/EJP.v1-14

Primary: 60K35
Secondary: 60J80

Keywords: branching processes , historical processes , Interacting diffusions , renormalization , super random walk

Vol.1 • 1996
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