FUNCTIONAL POISSON APPROXIMATION IN KANTOROVICH-RUBINSTEIN DISTANCE WITH APPLICATIONS TO U-STATISTICS AND STOCHASTIC GEOMETRY

• 成果类型: Article
• 署名作者: Decreusefond, Laurent; Schulte, Matthias; Thaele, Christoph
• 署名单位: IMT - Institut Mines-Telecom; Institut Polytechnique de Paris; Telecom Paris; Helmholtz Association; Karlsruhe Institute of Technology; Ruhr University Bochum
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/15-AOP1020
• 发表日期: 2016
• 页码: 2147-2197
• 关键词: point process-approximation; steins method; Wasserstein Distance; random-variables; bounds; limit; distributions; CONVERGENCE; SPACE

摘要

A Poisson or a binomial process on an abstract state space and a symmetric function f acting on k-tuples of its points are considered. They induce a point process on the target space of f. The main result is a functional limit theorem which provides an upper bound for an optimal transportation distance between the image process and a Poisson process on the target space. The technical background are a version of Stein's method for Poisson process approximation, a Glauber dynamics representation for the Poisson process and the Malliavin formalism. As applications of the main result, error bounds for approximations of U-statistics by Poisson, compound Poisson and stable random variables are derived, and examples from stochastic geometry are investigated.