TY  - JOUR
A1  - Zähle, Henryk
T1  - Space-time regularity of catalytic super-Brownian motion
N2  - The paper studies catalytic super-Brownian motion on the real line, where the branching rate is controlled by a catalyst. D. A. Dawson, K. Fleischmann and S. Roelly showed, for a broad class of catalysts, that, as for constant branching, the processes are absolutely continuous measures. This paper considers a class of catalysts, called moderate, which must satisfy a uniform boundedness condition and a condition controlling the degree of singularity---essentially that the mass of catalyst in small balls should (uniformly) be of order r^a, where a>0. The main result of this paper shows that for this class of catalysts there is a continuous density field for the process. Moreover the density is the unique solution (in law) of an appropriate SPDE.
Y1  - 2005
UR  - https://publishup.uni-potsdam.de/frontdoor/index/index/docId/13179
UR  - http://www.interscience.wiley.com/jpages/0025-584X/
ER  -