LOCAL-TIMES FOR SUPERDIFFUSIONS

• 成果类型: Article
• 署名作者: KRONE, SM
• 署名单位: University of Massachusetts System; University of Massachusetts Amherst
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/aop/1176989133
• 发表日期: 1993
• 页码: 1599-1623
• 关键词: super-brownian motion; partial-differential equations; continuity; DIFFUSIONS

摘要

In this work we study local times for a class of measure-valued Markov processes known as superprocesses. We begin by deriving analogues of well-known properties of ordinary local times. Then, restricting our attention to a class of superprocesses (which includes the important case of super-Brownian motion), we prove more detailed properties of the local times, such as joint continuity and a global Holder condition. These are then used to obtain path properties of the superprocesses themselves. For example, we compute the Hausdorff dimension of the ''level sets'' of super-Brownian motion.