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  - http://www.interscience.wiley.com/jpages/0025-584X/
ER  - 
TY  - JOUR
A1  - Zähle, Henryk
T1  - Heat equation with strongly inhomogeneous noise
N2  - The author considers the heat equation in dimension one with singular drift and inhomogeneous space-time white noise. In particular, the quadratic variation measure of the white noise is not required to be absolutely continuous w.r.t. the Lebesgue measure, neither in space nor in time. Under some assumptions the author gives statements on strong and weak existence as well as strong and weak uniqueness of continuous solutions.
Y1  - 2004
UR  - http://www.sciencedirect.com/science/journal/03044149
ER  -