Mathematics – Probability
Scientific paper
2008-06-16
Annales de l'Institut Henri Poincar\'e - Probabilit\'es et Statistiques 2008, Vol. 44, No. 3, 490-518
Mathematics
Probability
Published in at http://dx.doi.org/10.1214/07-AIHP155 the Annales de l'Institut Henri Poincar\'e - Probabilit\'es et Statistiqu
Scientific paper
10.1214/07-AIHP155
We study a spatial branching model, where the underlying motion is $d$-dimensional ($d\ge1$) Brownian motion and the branching rate is affected by a random collection of reproduction suppressing sets dubbed mild obstacles. The main result of this paper is the quenched law of large numbers for the population for all $d\ge1$. We also show that the branching Brownian motion with mild obstacles spreads less quickly than ordinary branching Brownian motion by giving an upper estimate on its speed. When the underlying motion is an arbitrary diffusion process, we obtain a dichotomy for the quenched local growth that is independent of the Poissonian intensity. More general offspring distributions (beyond the dyadic one considered in the main theorems) as well as mild obstacle models for superprocesses are also discussed.
No associations
LandOfFree
Quenched law of large numbers for branching Brownian motion in a random medium does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Quenched law of large numbers for branching Brownian motion in a random medium, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Quenched law of large numbers for branching Brownian motion in a random medium will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-91593