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

Marion Hesse; Andreas E. Kyprianou

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arXiv · 1308.1656

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

Marion Hesse·Andreas E. Kyprianou

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Abstract

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.

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Marion Hesse, Andreas E. Kyprianou. 2013-08-07. The total mass of super-Brownian motion upon exiting balls and Sheu's compact support condition. https://arxiv.org/abs/1308.1656

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