Dawson DA, Greven A (1996)
Publication Language: English
Publication Type: Journal article, Original article
Publication year: 1996
Publisher: Institute of Mathematical Statistics (IMS): OAJ / Institute of Mathematical Statistics
Book Volume: 1
Pages Range: 1-84
Journal Issue: 14
URI: https://projecteuclid.org/euclid.ejp/1453756477
DOI: 10.1214/EJP.v1-14
We study a class of systems of countably many linearly interacting diffusions whose components take values in [0, ∞) 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.
APA:
Dawson, D.A., & Greven, A. (1996). Multiple space-time scale analysis for interacting branching models. Electronic Journal of Probability, 1(14), 1-84. https://dx.doi.org/10.1214/EJP.v1-14
MLA:
Dawson, Donald Andrew, and Andreas Greven. "Multiple space-time scale analysis for interacting branching models." Electronic Journal of Probability 1.14 (1996): 1-84.
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