For a class of processes modeling the evolution of a spatially structured population with migration and a logistic local regulation of the reproduction dynamics, we show convergence to an upper invariant measure from a suitable class of initial distributions. It follows from recent work of Alison Etheridge that this upper invariant measure is nontrivial for sufficiently large super-criticality in the reproduction. For sufficiently small super-criticality, we prove local extinction by comparison with a mean field model. This latter result extends also to more general local reproduction regulations.
Publié le : 2007-04-14
Classification:
Interacting diffusions,
branching populations,
local competition,
extinction,
ergodic behavior,
60K35,
60J60,
60J80,
92D25
@article{1174323254,
author = {Hutzenthaler, M. and Wakolbinger, A.},
title = {Ergodic behavior of locally regulated branching populations},
journal = {Ann. Appl. Probab.},
volume = {17},
number = {1},
year = {2007},
pages = { 474-501},
language = {en},
url = {http://dml.mathdoc.fr/item/1174323254}
}
Hutzenthaler, M.; Wakolbinger, A. Ergodic behavior of locally regulated branching populations. Ann. Appl. Probab., Tome 17 (2007) no. 1, pp. 474-501. http://gdmltest.u-ga.fr/item/1174323254/