TY - JOUR
T1 - The mass of super-Brownian motion upon exiting balls and Sheu's compact support condition
AU - Hesse, Marion
AU - Kyprianou, Andreas E.
PY - 2014/6/1
Y1 - 2014/6/1
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.
UR - http://www.scopus.com/inward/record.url?scp=84894345440&partnerID=8YFLogxK
UR - http://dx.doi.org/10.1016/j.spa.2014.01.011
U2 - 10.1016/j.spa.2014.01.011
DO - 10.1016/j.spa.2014.01.011
M3 - Article
AN - SCOPUS:84894345440
SN - 0304-4149
VL - 124
SP - 2003
EP - 2022
JO - Stochastic Processes and their Applications
JF - Stochastic Processes and their Applications
IS - 6
ER -