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 Electronic Journal of Probability > Vol. 1 (1996) > Paper 14 open journal systems 


Multiple Space-Time Scale Analysis For Interacting Branching Models

Donald A. Dawson, Carleton University
Andreas Greven, Universitat Erlangen-Nurnberg


Abstract
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.


Full text: PDF

Pages: 1-84

Published on: February 28, 1996
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Electronic Journal of Probability. ISSN: 1083-6489