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

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
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Submitted on : Friday, September 13, 2019 - 4:20:26 PM
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  • 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⟩

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