GIRSANOV IDENTITIES FOR POISSON MEASURES UNDER QUASI-NILPOTENT TRANSFORMATIONS

• 成果类型: Article
• 署名作者: Privault, Nicolas
• 署名单位: Nanyang Technological University
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/10-AOP640
• 发表日期: 2012
• 页码: 1009-1040
• 关键词: integrals; FORMULA; SPACE

摘要

We prove a Girsanov identity on the Poisson space for anticipating transformations that satisfy a strong quasi-nilpotence condition. Applications are given to the Girsanov theorem and to the invariance of Poisson measures under random transformations. The proofs use combinatorial identities for the central moments of Poisson stochastic integrals.