WIAS Preprint No. 1878, (2013)

The total mass of super-Brownian motion upon exiting balls and Sheu's compact support condition


  • Hesse, Marion
  • Kyprianou, Andreas

2010 Mathematics Subject Classification

  • 60J68 60J80


  • super-Brownian motion, exit measures, time-dependent continuous state branching processes, 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 total mass process is a time-inhomogeneous continuous-state branching process, where the increasing radii of the balls are taken as the time-parameter. We 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 identify the compact support criterion in Sheu (1994) as Grey's condition (1974) for the aforementioned limiting branching mechanism.

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