In this paper we will investigate the long time behavior of critical
branching Brownian motion and (finite variance) super-Brownian motion (the
so-called Dawson-Watanabe process) on $\mathbb{R}$^d$. These processes are
known to be persistent if $d \geq 3$; that is, there exist nontrivial
equilibrium measures. If $d \leq 2$, they cluster; that is, the processes
converge to the 0 configuration while the surviving mass piles up in so-called
clusters.
¶ We study the spatial profile of the clusters in the
“critical” dimension $d = 2$ via multiple space scale analysis.
We will also investigate the long-time behavior of these models restricted to
finite boxes in $d \geq 2$. On the way, we develop coupling and comparison
methods for spatial branching models.
@article{1023481107,
author = {Klenke, Achim},
title = {Multiple scale analysis of clusters in spatial branching
models},
journal = {Ann. Probab.},
volume = {25},
number = {4},
year = {1997},
pages = { 1670-1711},
language = {en},
url = {http://dml.mathdoc.fr/item/1023481107}
}
Klenke, Achim. Multiple scale analysis of clusters in spatial branching
models. Ann. Probab., Tome 25 (1997) no. 4, pp. 1670-1711. http://gdmltest.u-ga.fr/item/1023481107/