Palm measure duality and conditioning in regenerative sets
成果类型：
Article
署名作者：
Kallenberg, O
署名单位：
Auburn University System; Auburn University
刊物名称：
ANNALS OF PROBABILITY
ISSN/ISSBN：
0091-1798
DOI：
10.1214/aop/1022677391
发表日期：
1999
页码：
945-969
关键词：
摘要：
For a simple point process Xi on a suitable topological space, the associated Palm distribution at a point s may be approximated by the conditional distribution, given that Xi hits a small neighborhood of s. To study the corresponding approximation problem for more general random sets, we develop a general duality theory, which allows the Palm distributions with respect to an associated random measure to be expressed in terms of conditional densities with suitable martingale and continuity properties. The stated approximation property then becomes equivalent to a certain asymptotic relation involving conditional hitting probabilities. As an application, we consider the Palm distributions of regenerative sets with respect to their local time random measures.