| Título: | Hydrodynamic Limit Fluctuations of Super-Brownian Motion with a Stable Catalyst |
| Autores: |
Fleischmann, Klaus; Weierstrass Institute for Applied Analysis and Stochastics, Berlin Mörters, Peter; University of Bath Wachtel, Vitali; Weierstrass Institute for Applied Analysis and Stochastics, Berlin |
| Fecha: | 2006-01-01 |
| Publicador: | Electronic journal of probability |
| Fuente: |
 |
| Tipo: |
Peer-reviewed Article |
| Tema: |
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 60G57; 60J80; 60K35 |
| Descripción: | 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. |
| Idioma: | No aplica |
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