ON THE PARABOLIC MARTIN BOUNDARY OF THE ORNSTEIN-UHLENBECK OPERATOR ON WIENER SPACE

• 成果类型: Article
• 署名作者: ROCKNER, M
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/aop/1176989818
• 发表日期: 1992
• 页码: 1063-1085
• 关键词: classical dirichlet forms; topological vector-spaces; harmonic-functions; characterize; DIFFUSIONS

摘要

We study the positive parabolic functions of the Ornstein-Uhlenbeck operator on an abstract Wiener space E using the approach developed by Dynkin. This involves first proving a characterization of the entrance space of the corresponding Ornstein-Uhlenbeck semigroup and deriving an integral representation for an arbitrary entrance law in terms of extreme ones. It is shown that the Cameron-Martin densities are extreme parabolic functions, but that if dim E = infinity, not every positive parabolic function has an integral representation in terms of those (which is in contrast to the finite-dimensional case). Furthermore, conditions for a parabolic function to be representable in terms of Cameron-Martin densities are proved.