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On the occupation measure of super-Brownian motion. (English) Zbl 1110.60083

Summary: We derive the asymptotic behavior of the total occupation measure of the unit ball for super-Brownian motion started from the Dirac measure at a distant point and conditioned to hit the unit ball. In the critical dimension 4, we obtain a limiting exponential distribution.

MSC:

60J80 Branching processes (Galton-Watson, birth-and-death, etc.)
82B41 Random walks, random surfaces, lattice animals, etc. in equilibrium statistical mechanics
60G57 Random measures