Mass-time-space scaling of a super-Brownian catalyst reactant pair
- Fleischmann, Klaus
- Xiong, Jie
2010 Mathematics Subject Classification
- 60K35 60G57 60J80
- Catalyst, reactant, superprocess, martingale problem, stochastic equation, density field, collision measure, colision local time, extinction, critical scaling
The one-dimensional super-Brownian reactant Xϱ with a super-Brownian catalyst ϱ has a jointly continuous density field satisfying a stochastic partial differential equation. Consider any expectation preserving mass-time-space scaling of Xϱ. Using the density field, one can pass to an fdd scaling limit of the measure-valued process, which degenerates also under the critical scaling of ϱ. For some of the scaling indexes, convergence on path spaces holds, too.
- J. Theoret. Probab., 19 (2006) pp. 557-588.