We relate the recurrence and transience of a branching diffusion process on
a Riemannian manifold M to some properties of a linear elliptic operator
onM (including spectral properties). There is a trade-off between the
tendency of the transient Brownian motion to escape and the birth process of
the new particles. If the latter has a high enough intensity then it may
override the transience of the Brownian motion, leading to the recurrence of
the branching process, and vice versa. In the case of a spherically
symmetric manifold, the critical intensity of the population growth can be
found explicitly.
Publié le : 2003-01-14
Classification:
Branching process,
Brownian motion,
Riemannian manifold,
recurrence,
transience,
maximum principle,
gauge,
58J65,
60J80
@article{1046294311,
author = {Grigor'yan, Alexander and Kelbert, Mark},
title = {Recurrence and transience of branching diffusion processes on Riemannian manifolds},
journal = {Ann. Probab.},
volume = {31},
number = {1},
year = {2003},
pages = { 244-284},
language = {en},
url = {http://dml.mathdoc.fr/item/1046294311}
}
Grigor'yan, Alexander; Kelbert, Mark. Recurrence and transience of branching diffusion processes on Riemannian manifolds. Ann. Probab., Tome 31 (2003) no. 1, pp. 244-284. http://gdmltest.u-ga.fr/item/1046294311/