GIRSANOV TRANSFORM FOR SYMMETRICAL DIFFUSIONS WITH INFINITE-DIMENSIONAL STATE-SPACE

• 成果类型: Article
• 署名作者: ALBEVERIO, S; ROCKNER, M; ZHANG, TS
• 署名单位: University of Bonn; University of Edinburgh
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/aop/1176989277
• 发表日期: 1993
• 页码: 961-978
• 关键词: classical dirichlet forms; topological vector-spaces

摘要

A Cameron-Martin-Girsanov-Maruyama type formula for symmetric diffusions on infinite dimensional state space is proved. In particular, relaxations of the usual assumptions which still imply absolute continuity (but possibly no longer equivalence) of the path space measures are discussed. In addition a converse result is proved, that is, we show that absolute continuity of the path space measures enables us to identify the underlying Dirichlet form.