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 Electronic Journal of Probability > Vol. 11 (2006) > Paper 29 open journal systems 


Hydrodynamic limit fluctuations of super-Brownian motion with a stable catalyst

Klaus Fleischmann, Weierstrass Institute for Applied Analysis and Stochastics, Berlin
Peter Mörters, University of Bath
Vitali Wachtel, Weierstrass Institute for Applied Analysis and Stochastics, Berlin


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+γ, where γ ∈ (0,1) is an index associated to the medium.


Full text: PDF

Pages: 723-767

Published on: August 27, 2006
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Electronic Journal of Probability. ISSN: 1083-6489