WIAS Preprint No. 619, (2000)

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.

Appeared in

  • Teor. Veroyatnost. i Primenen 47 (2002), pp. 417-451

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