Electronic Journal of Probability

Multiple Space-Time Scale Analysis For Interacting Branching Models

Donald Dawson and Andreas Greven

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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.

Article information

Electron. J. Probab., Volume 1 (1996), paper no. 14, 84 pp.

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]
Secondary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)

Branching processes interacting diffusions super random walk renormalization historical processes

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Dawson, Donald; Greven, Andreas. Multiple Space-Time Scale Analysis For Interacting Branching Models. Electron. J. Probab. 1 (1996), paper no. 14, 84 pp. doi:10.1214/EJP.v1-14. https://projecteuclid.org/euclid.ejp/1453756477

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