A super-Brownian motion with a locally infinite catalytic mass
- Fleischmann, Klaus
- Mueller, Carl
2010 Mathematics Subject Classification
- 60J80 60J55 60G57
- hyperbolic branching rate, strong killing, infinite point catalyst, Feynman-Kac equation, killed Brownian motion, historical process, super-Brownian motion, superprocess, branching functional of infinite (local) characteristic, measure-valued branching, catalytic superprocess
dXt = ½ ΔXt dt + √2ρ2XtdWt, t ≥ 0, (1)
(with a space-time white noise W).
If the finite starting measure X0 does not have mass at b = 0, then this superprocess X will never hit the catalytic center: There is Brownian stopping time r strictly smaller than the hitting time of 0 such that Dynkin's stopped measures Xr vanishes except a.s.
- Probab. Theory Related Fields, 107 (1997), pp. 325-357