Large scale localization of a spatial version of Neveu's branching process
- Fleischmann, Klaus
- Wachtel, Vitali
2010 Mathematics Subject Classification
- 60J80 60G57
- Neveu's continuous-state branching, infinite mean branching superprocess, large scale concentration in one point, log-Laplace product formula, small epsilon asymptotics
Recently a spatial versions of Neveu's (1992) continuous-state branching process was constructed by Fleischmann and Sturm (2004). This superprocess with infinite mean branching behaves quite differently from usual supercritical spatial branching processes. In fact, at macroscopic scales, the mass renormalized to a (random) probability measure is concentrated in a single space point which randomly fluctuates according to the underlying symmetric stable motion process.
- Electron. J. Probab., 11 (2006) pp. 723-767.