Poisson process Fock space representation, chaos expansion and covariance inequalities

• 成果类型: Article
• 署名作者: Last, Guenter; Penrose, Mathew D.
• 署名单位: Helmholtz Association; Karlsruhe Institute of Technology; University of Bath
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-010-0288-5
• 发表日期: 2011
• 页码: 663-690
• 关键词: deviation inequalities; normal approximation; functionals; IDENTITIES

摘要

We consider a Poisson process eta on an arbitrary measurable space with an arbitrary sigma-finite intensity measure. We establish an explicit Fock space representation of square integrable functions of eta. As a consequence we identify explicitly, in terms of iterated difference operators, the integrands in the Wiener-It chaos expansion. We apply these results to extend well-known variance inequalities for homogeneous Poisson processes on the line to the general Poisson case. The Poincar, inequality is a special case. Further applications are covariance identities for Poisson processes on (strictly) ordered spaces and Harris-FKG-inequalities for monotone functions of eta.