@article{EJP348,
author = {Klaus Fleischmann and Peter Mörters and Vitali Wachtel},
title = {Hydrodynamic Limit Fluctuations of Super-Brownian Motion with a Stable Catalyst},
journal = {Electron. J. Probab.},
fjournal = {Electronic Journal of Probability},
volume = {11},
year = {2006},
keywords = {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},
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.},
pages = {no. 29, 723-767},
issn = {1083-6489},
doi = {10.1214/EJP.v11-348},
url = {http://ejp.ejpecp.org/article/view/348}}