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

Marion Hesse; Andreas E. Kyprianou

doi:10.1016/j.spa.2014.01.011

The 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 mass of a d-dimensional super-Brownian motion as it first exits an increasing sequence of balls. The 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 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.

Original language	English
Pages (from-to)	2003-2022
Number of pages	20
Journal	Stochastic Processes and their Applications
Volume	124
Issue number	6
Early online date	7 Feb 2014
DOIs	https://doi.org/10.1016/j.spa.2014.01.011
Publication status	Published - 1 Jun 2014

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10.1016/j.spa.2014.01.011

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abstract = "We study the mass of a d-dimensional super-Brownian motion as it first exits an increasing sequence of balls. The 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 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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AU - Kyprianou, Andreas E.

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N2 - We study the mass of a d-dimensional super-Brownian motion as it first exits an increasing sequence of balls. The 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 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.

AB - We study the mass of a d-dimensional super-Brownian motion as it first exits an increasing sequence of balls. The 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 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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UR - http://dx.doi.org/10.1016/j.spa.2014.01.011

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EP - 2022

JO - Stochastic Processes and their Applications

JF - Stochastic Processes and their Applications

IS - 6

ER -

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

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