Branching systems with long living particles at the critical dimension
- Fleischmann, Klaus
- Vatutin, Vladimir A.
- Wakolbinger, Anton
2010 Mathematics Subject Classification
- 60J80 60G70 60J15
- branching particle system, critical dimension, limit theorem, long living particles, absolute continuity, random density, superprocess, persistence, mixed Poissonian particle system, residual lifetime process, stable subordinator
A spatial branching process is considered in which particles have a life time law with a tail index smaller than one. Other than in classical branching particle systems, at the critical dimension the system does not suffer local extinction when started from a spatially homogenous initial population. In fact, persistent convergence to a mixed Poissonian system is shown. The random limiting intensity is characterized in law by the random density in a space point of a related age-dependent superprocess at a fixed time. The proof relies on a refined study of the system starting from asymptotically large but finite initial populations.
- Teor. Veroyatnost. i Primenen 47 (2002), pp. 417-451