@article{EJP14,
author = {Donald Dawson and Andreas Greven},
title = {Multiple Space-Time Scale Analysis For Interacting Branching Models},
journal = {Electron. J. Probab.},
fjournal = {Electronic Journal of Probability},
volume = {1},
year = {1996},
keywords = {Branching processes, interacting diffusions, super random walk, renormalization, historical processes},
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.},
pages = {no. 14, 1-84},
issn = {1083-6489},
doi = {10.1214/EJP.v1-14},
url = {http://ejp.ejpecp.org/article/view/14}}