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2006 Hydrodynamic Limit Fluctuations of Super-Brownian Motion with a Stable Catalyst
Klaus Fleischmann, Peter Mörters, Vitali Wachtel
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Electron. J. Probab. 11: 723-767 (2006). DOI: 10.1214/EJP.v11-348

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.

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Klaus Fleischmann. Peter Mörters. Vitali Wachtel. "Hydrodynamic Limit Fluctuations of Super-Brownian Motion with a Stable Catalyst." Electron. J. Probab. 11 723 - 767, 2006. https://doi.org/10.1214/EJP.v11-348

Information

Accepted: 27 August 2006; Published: 2006
First available in Project Euclid: 31 May 2016

zbMATH: 1110.60082
MathSciNet: MR2242662
Digital Object Identifier: 10.1214/EJP.v11-348

Subjects:
Primary: 60G57
Secondary: 60J80 , 60K35

Keywords: Catalyst , Catalytic branching , critical scaling , generalised stable Ornstein-Uhlenbeck process , index jump , parabolic Anderson model with sta , random environment , reactant , refined law of large numbers , stable medium , supercritical dimension , Superprocess

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