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

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dc.creatorFleischmann, Klaus
dc.creatorMoerters, Peter
dc.creatorWachtel, Vitali
dc.date2005-08-19
dc.date.accessioned2026-07-07T05:22:30Z
dc.date.available2026-07-07T05:22:30Z
dc.descriptionWe 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.
dc.description40 pages
dc.identifierhttps://arxiv.org/abs/math/0508368
dc.identifierhttp://arxiv.org/abs/math/0508368
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/76086
dc.subjectProbability
dc.subject60G57; 60J80; 60K35
dc.titleHydrodynamic limit fluctuations of super-Brownian motion with a stable catalyst
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