Abstract : 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.
https://hal.archives-ouvertes.fr/hal-01010967 Contributor : Laurent DecreusefondConnect in order to contact the contributor Submitted on : Tuesday, February 24, 2015 - 2:04:43 PM Last modification on : Wednesday, November 3, 2021 - 6:18:13 AM Long-term archiving on: : Thursday, May 28, 2015 - 4:35:48 PM
Laurent Decreusefond, Matthias Schulte, Christoph Thäle. Functional Poisson approximation in Kantorovich-Rubinstein distance with applications to U-statistics and stochastic geometry. Annals of Probability, Institute of Mathematical Statistics, 2016, 44 (3), pp.2147-2197. ⟨10.1214/15-AOP1020⟩. ⟨hal-01010967v2⟩