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

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

2005-08-19

arxiv.org/abs/math/0508368v1

Mathematics

Probability

40 pages

Scientific paper

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 is an index associated to the medium.

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