Finite time extinction of super-Brownian motions with catalysts
| dc.creator | Dawson, Donald A. | |
| dc.creator | Fleischmann, Klaus | |
| dc.creator | Mueller, Carl | |
| dc.date | 1998-09-21 | |
| dc.date.accessioned | 2026-07-07T05:26:05Z | |
| dc.date.available | 2026-07-07T05:26:05Z | |
| dc.description | Consider a catalytic super-Brownian motion $X=X^Γ$ with finite variance branching. Here `catalytic' means that branching of the reactant $X$ is only possible in the presence of some catalyst. Our intrinsic example of a catalyst is a stable random measure $Γ$ on $R$ of index $0< gamma <1$. Consequently, here the catalyst is located in a countable dense subset of $R$. Starting with a finite reactant mass $X_0$ supported by a compact set, $X$ is shown to die in finite time. Our probabilistic argument uses the idea of good and bad historical paths of reactant `particles' during time periods $[T_{n},T_{n+1})$. Good paths have a significant collision local time with the catalyst, and extinction can be shown by individual time change according to the collision local time and a comparison with Feller's branching diffusion. On the other hand, the remaining bad paths are shown to have a small expected mass at time $T_{n+1}$ which can be controlled by the hitting probability of point catalysts and the collision local time spent on them. | |
| dc.description | 36 pages, 1 figure (which might not completely be reflected) | |
| dc.identifier | https://arxiv.org/abs/math/9809115 | |
| dc.identifier | http://arxiv.org/abs/math/9809115 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/77421 | |
| dc.subject | Probability | |
| dc.subject | 60J80 60J55 60G57 | |
| dc.title | Finite time extinction of super-Brownian motions with catalysts | |
| dc.type | text |