Geodesic
Branching systems with long-living particles at the critical dimension
Teoriâ veroâtnostej i ee primeneniâ, Tome 47 (2002) no. 3, pp. 417-451

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A spatial branching process is considered in which particles have a lifetime law with a tail index smaller than one. It is shown that at the critical dimension, unlike classical branching particle systems the population does not suffer local extinction when started from a spatially homogeneous Poissonian initial population. In fact, persistent convergence to a mixed Poissonian particle system is shown. The random intensity of the limiting process 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.
Keywords: branching particle system, residual lifetime process, stable subordinator, critical dimension, limit theorem, long-living particles, absolute continuity, random density, mixed Poissonian particle system.
Mots-clés : superprocess, persistence 
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     title = {Branching systems with long-living particles at the critical dimension},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
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     year = {2002},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2002_47_3_a0/}
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A. Wakolbinger; V. A. Vatutin; K. Fleischmann. Branching systems with long-living particles at the critical dimension. Teoriâ veroâtnostej i ee primeneniâ, Tome 47 (2002) no. 3, pp. 417-451. http://geodesic.mathdoc.fr/item/TVP_2002_47_3_a0/