The divergence of Banach space valued random variables on Wiener space

• 成果类型: Article
• 署名作者: Mayer-Wolf, E; Zakai, M
• 署名单位: Technion Israel Institute of Technology; Technion Israel Institute of Technology
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-004-0397-0
• 发表日期: 2005
• 页码: 291-320
• 关键词: tangent processes; differential-equations; vector-fields; FLOWS

摘要

The domain of definition of the divergence operator delta on an abstract Wiener space (W, H, mu) is extended to include W - valued and W x W - valued integrands. The main properties and characterizations of this extension are derived and it is shown that in some sense the added elements in delta' s extended domain have divergence zero. These results are then applied to the analysis of quasiinvariant flows induced by W-valued vector fields and, among other results, it turns out that these divergence-free vector fields are responsible for generating measure preserving flows.