In this paper we consider a multilevel branching diffusion particle system and its diffusion approximation, which can be characterized as an $M(M(R^d))$-valued process. The long term behavior of the limiting process is studied. The main results are that if $d \leq 4$, then the two level $M(M(R^d))$-valued process suffers local extinction, and if $d = 4$, then the process has a self-similarity property.
Publié le : 1994-04-14
Classification:
Multilevel branching diffusion,
two level measure-valued process,
local extinction,
rescaleld process,
self-similarity property,
60J80,
60J60,
60J65,
60J57,
60F05,
60H15,
35C15
@article{1176988733,
author = {Wu, Yadong},
title = {Asymptotic Behavior of the Two Level Measure Branching Process},
journal = {Ann. Probab.},
volume = {22},
number = {4},
year = {1994},
pages = { 854-874},
language = {en},
url = {http://dml.mathdoc.fr/item/1176988733}
}
Wu, Yadong. Asymptotic Behavior of the Two Level Measure Branching Process. Ann. Probab., Tome 22 (1994) no. 4, pp. 854-874. http://gdmltest.u-ga.fr/item/1176988733/