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 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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