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

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:124

Article

Hesse, Marion¹  Kyprianou, Andreas E.¹ 

[1] Univ Bath, Bath BA2 7AY, Avon, England

关键词: Super-Brownian motion;    Exit measures;    Time-dependent continuous state branching processes;    Compact support condition;   

DOI  :  10.1016/j.spa.2014.01.011

来源: Elsevier

【 摘 要 】

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. (C) 2014 Elsevier B.V. All rights reserved.

【 授权许可】

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