THE COMPOSITION OF WIENER FUNCTIONALS WITH NON-ABSOLUTELY CONTINUOUS SHIFTS

• 成果类型: Article
• 署名作者: USTUNEL, AS; ZAKAI, M
• 署名单位: Technion Israel Institute of Technology
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/BF01192512
• 发表日期: 1994
• 页码: 163-184
• 关键词: malliavin calculus

摘要

In this paper we study some classes of Wiener functionals whose elements can be composed with a non-linear, non-absolutely continous transformation of the form of perturbation of identity in the direction of Cameron-Martin space, We show that under certain conditions the image of the Wiener measure under the above transformation induces a generalized Wiener functional on certain Sobolev spaces generalizing the Radon-Nikodym relation to non absolutely continuous transformations. A series representation for the generalized Radon-Nikodym derivative is presented and conditional expectations of some generalized random variables are considered.