Strong clumping of super-Brownian motion in a stable catalytic medium
type: Item
instance of: scholarly article
title: Strong clumping of super-Brownian motion in a stable catalytic medium
zbMATH Open document ID: 1029.60088
author: Donald A. Dawson
author: Klaus Fleischmann
author: Peter Mörters
published in: The Annals of Probability
publication date: 2003-05-06T00:00:00Z
review text: The authors study the evolution of the mass of clusters at spatially rare sites developped by the long time behaviour of the continuous super-Brownian motion in a stable catalytic medium. The mass of each cluster evolves independently according to a non-Markovian continuous process trapped at mass zero, which is described by means of a Brwonian snake construction in random medium. The authors give a functional limit theorem which describes the phenomenon: As a limit one obtains a Poisson point field of mass clusters with no spatial motion component and with infinite variance. Survival probabilities and asymptotic sizes are also studied.
reviewed by: Mihai Gradinaru
Mathematics Subject Classification ID: 60K37
Mathematics Subject Classification ID: 60F05
Mathematics Subject Classification ID: 60G57
Mathematics Subject Classification ID: 60J80
Mathematics Subject Classification ID: 60K35
zbMATH DE Number: 1906108
zbMATH Keywords: catalytic super-Brownian motion
zbMATH Keywords: stable catalysts
zbMATH Keywords: critical branching
zbMATH Keywords: measure-valued branching
zbMATH Keywords: random medium
zbMATH Keywords: clumping
zbMATH Keywords: functional limit law
zbMATH Keywords: historical superprocess
zbMATH Keywords: Brownian snake in a random medium
zbMATH Keywords: subordination
zbMATH Keywords: exit measures
zbMATH Keywords: good and bad paths
zbMATH Keywords: stopped measures
zbMATH Keywords: collision local time
zbMATH Keywords: heavy tails
zbMATH Keywords: Feynman-Kac formula
zbMATH Keywords: annealed and quenched random medium approaches
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aop/1039548380
OpenAlex ID: W2013118524
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DOI: 10.1214/AOP/1039548380
description: scientific article; zbMATH DE number 1906108