2002-10-01
Strong clumping of super-Brownian motion in a stable catalytic medium
Publication
Publication
Annals of Probability
,
Volume 30
-
Issue 4
p. 1990-
2045
A typical feature of the long time behavior of continuous super-Brownian motion in a stable catalytic medium is the development of large mass clumps (or clusters) at spatially rare sites. We describe this phenomenon by means of a functional limit theorem under renormalization. The limiting process is a Poisson point field of mass clumps with no spatial motion component and with infinite variance. The mass of each cluster evolves independently according to a non-Markovian continuous process trapped at mass zero, which we describe explicitly by means of a Brownian snake construction in a random medium. We also determine the survival probability and asymptotic size of the clumps.
| Additional Metadata | |
|---|---|
| Keywords | Brownian snake in a random medium, Catalytic super-Brownian motion, Clumping, Critical branching, Exit measures, Functional limit law, Historical superprocess, Measure-valued branching, Random medium, Stable catalysts, Subordination |
| Persistent URL | dx.doi.org/10.1214/aop/1039548380 |
| Journal | Annals of Probability |
| Citation |
Dawson, D.A, Fleischmann, K. (Klaus), & Mörters, P. (Peter). (2002). Strong clumping of super-Brownian motion in a stable catalytic medium. Annals of Probability, 30(4), 1990–2045. doi:10.1214/aop/1039548380
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