125 research outputs found
The total mass of super-Brownian motion upon exiting balls and Sheu's compact support condition
We study the total mass of a d-dimensional super-Brownian motion as it first
exits an increasing sequence of balls. The process of the total mass is a
time-inhomogeneous continuous-state branching process, where the increasing
radii of the balls are taken as the time parameter. We are able to characterise
its time-dependent branching mechanism and show that it converges, as time goes
to infinity, towards the branching mechanism of the total mass of a
one-dimensional super-Brownian motion as it first crosses above an increasing
sequence of levels. Our results allow us to identify the compact support
criterion given in Sheu (1994) as a classical Grey condition (1974) for the
aforementioned limiting branching mechanism.Comment: 28 pages, 2 figure
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