# Functional Poisson approximation in Kantorovich-Rubinstein distance with applications to U-statistics and stochastic geometry

1 DIG - Data, Intelligence and Graphs
LTCI - Laboratoire Traitement et Communication de l'Information
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 dynamic 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.

Document type :
Journal articles
Domain :

https://hal.telecom-paristech.fr/hal-02286899
Contributor : Telecomparis Hal <>
Submitted on : Friday, September 13, 2019 - 4:20:26 PM
Last modification on : Thursday, October 17, 2019 - 12:36:59 PM

### Identifiers

• HAL Id : hal-02286899, version 1

### Citation

Laurent Decreusefond, Matthias Schülte, Christoph Thäle. Functional Poisson approximation in Kantorovich-Rubinstein distance with applications to U-statistics and stochastic geometry. Annals of Probability, 2016, 44 (3), pp.2147-2197. ⟨hal-02286899⟩

Record views