In a one-dimensional single point-catalytic continuous super-Brownian motion studied by Dawson and Fleischmann, the occupation density measure $\lambda^c$ at the catalyst's position $\mathcal{C}$ is shown to be a singular (diffuse) random measure. The source of this qualitative new effect is the irregularity of the varying medium $\delta_\mathcal{C}$ 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-Khintchine representation of $\lambda^\mathcal{C}$ 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.
Publié le : 1995-01-14
Classification:
Point catalytic medium,
critical branching,
super-Brownian local time,
occupation time,
occupation density,
measure-valued branching,
superprocess,
60J80,
60J65,
60G57
@article{1176988375,
author = {Dawson, Donald A. and Fleischmann, Klaus and Li, Yi and Mueller, Carl},
title = {Singularity of Super-Brownian Local Time at a Point Catalyst},
journal = {Ann. Probab.},
volume = {23},
number = {3},
year = {1995},
pages = { 37-55},
language = {en},
url = {http://dml.mathdoc.fr/item/1176988375}
}
Dawson, Donald A.; Fleischmann, Klaus; Li, Yi; Mueller, Carl. Singularity of Super-Brownian Local Time at a Point Catalyst. Ann. Probab., Tome 23 (1995) no. 3, pp. 37-55. http://gdmltest.u-ga.fr/item/1176988375/