Singularity of super-Brownian local time at a point catalyst

In an one-dimensional single point-catalytic continuous super-Brownian motion studied by Dawson and Fleischmann (1993), the occupation density measure #lambda#"#sigma# at the catalyst's position #sigma# is shown to be a singular (diffuse) random measure. The source of this qualitative new effect is the irregularity of the varying medium #delta#_#sigma#, describing the point catalyst. The proof is based on a probabilistic characterization of the law of the Palm canonical clusters #chi# appearing in the Levy-Khinchin representation of #lambda#"#sigma# in a historical process setting and the fact that these #chi# have infinite left upper density (with respect to Lebesgue measure) at the Palm time point. (orig.)Available from TIB Hannover: RR 5549(56)+a / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman