A CLASS OF PATH-VALUED MARKOV-PROCESSES AND ITS APPLICATIONS TO SUPERPROCESSES

• 成果类型: Article
• 署名作者: LEGALL, JF
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/BF01197336
• 发表日期: 1993
• 页码: 25-46
• 关键词: super-brownian motion

摘要

Let (xi(S)) be a continuous Markov process satisfying certain regularity assumptions. We introduce a path-valued strong Markov process associated with (xi(S)), which is closely related to the so-called superprocess with spatial motion (xi(S)). In particular, a subset H of the state space of (xi(S)) intersects the range of the superprocess if and only if the set of paths that hit H is not polar for the path-valued process. The latter property can be investigated using the tools of the potential theory of symmetric Markov processes: A set is not polar if and only if it supports a measure of finite energy. The same approach can be applied to study sets that are polar for the graph of the superprocess. In the special case when (xi(S)) is a diffusion process, we recover certain results recently obtained by Dynkin.