CONDITIONING SUPER-BROWNIAN MOTION ON ITS BOUNDARY STATISTICS, AND FRAGMENTATION
成果类型：
Article
署名作者：
Salisbury, Thomas S.; Sezer, A. Deniz
署名单位：
York University - Canada; University of Calgary
刊物名称：
ANNALS OF PROBABILITY
ISSN/ISSBN：
0091-1798
DOI：
10.1214/12-AOP778
发表日期：
2013
页码：
3617-3657
关键词：
摘要：
We condition super-Brownian motion on boundary statistics of the exit measure X-D from a bounded domain D. These are random variables defined on an auxiliary probability space generated by sampling from the exit measure X-D. Two particular examples are: conditioning on a Poisson random measure with intensity beta X-D and conditioning on X-D itself. We find the conditional laws as h-transforms of the original SBM law using Dynkin's formulation of X-harmonic functions. We give explicit expression for the (extended) X-harmonic functions considered. We also obtain explicit constructions of these conditional laws in terms of branching particle systems. For example, we give a fragmentation system description of the law of SBM conditioned on X-D = nu, in terms of a particle system, called the backbone. Each particle in the backbone is labeled by a measure 1 (nu) over tilde, representing its descendants' total contribution to the exit measure. The particle's spatial motion is an h-transform of Brownian motion, where h depends on (nu) over tilde. At the particle's death two new particles are born, and ($) over tilde is passed to the newborns by fragmentation.