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Hydrodynamic Limit Fluctuations of Super-Brownian Motion with a Stable Catalyst

Dublin Core		PKP Metadata Items	Metadata for this Document
1.	Title	Title of document	Hydrodynamic Limit Fluctuations of Super-Brownian Motion with a Stable Catalyst
2.	Creator	Author's name, affiliation, country	Klaus Fleischmann; Weierstrass Institute for Applied Analysis and Stochastics, Berlin
2.	Creator	Author's name, affiliation, country	Peter Mörters; University of Bath
2.	Creator	Author's name, affiliation, country	Vitali Wachtel; Weierstrass Institute for Applied Analysis and Stochastics, Berlin
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)	Catalyst, reactant, superprocess, critical scaling, refined law of large numbers, catalytic branching, stable medium, random environment, supercritical dimension, generalised stable Ornstein-Uhlenbeck process, index jump, parabolic Anderson model with sta
3.	Subject	Subject classification	60G57; 60J80; 60K35
4.	Description	Abstract	We consider the behaviour of a continuous super-Brownian motion catalysed by a random medium with infinite overall density under the hydrodynamic scaling of mass, time, and space. We show that, in supercritical dimensions, the scaled process converges to a macroscopic heat flow, and the appropriately rescaled random fluctuations around this macroscopic flow are asymptotically bounded, in the sense of log-Laplace transforms, by generalised stable Ornstein-Uhlenbeck processes. The most interesting new effect we observe is the occurrence of an index-jump from a Gaussian situation to stable fluctuations of index $1+\gamma$, where $\gamma \in (0,1)$ is an index associated to the medium.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)	DFG, EPSRC grant EP/C500229/1, and an EPSRC Advanced Research Fellowship
7.	Date	(YYYY-MM-DD)	2006-08-27
8.	Type	Status & genre	Peer-reviewed Article
8.	Type	Type
9.	Format	File format	PDF
10.	Identifier	Uniform Resource Identifier	http://ejp.ejpecp.org/article/view/348
10.	Identifier	Digital Object Identifier	10.1214/EJP.v11-348
11.	Source	Journal/conference title; vol., no. (year)	Electronic Journal of Probability; Vol 11
12.	Language	English=en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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