Pinning class of the Wiener measure by a functional: related martingales and invariance properties

• 成果类型: Article
• 署名作者: Baudoin, F; Thieullen, M
• 署名单位: Technische Universitat Wien; Universite Paris Cite; Sorbonne Universite
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-003-0280-4
• 发表日期: 2003
• 页码: 1-36
• 关键词: STOCHASTIC DIFFERENTIAL-EQUATIONS; geometric brownian motions; reciprocal diffusions; MARKOV-PROCESSES; symmetries

摘要

For a given functional Y on the path space, we define the pinning class of the Wiener measure as the class of probabilities which admit the same conditioning given Y as the Wiener measure. Using stochastic analysis and the theory of initial enlargement of filtration, we study the transformations (not necessarily adapted) which preserve this class. We prove, in this non Markov setting, a stochastic Newton equation and a stochastic Noether theorem. We conclude the paper with some non canonical representations of Brownian motion, closely related to our study.