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Pré-Publication, Document De Travail Année : 2014

Functional Poisson approximation in Rubinstein distance

Résumé

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.
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Dates et versions

hal-01010967 , version 1 (21-06-2014)
hal-01010967 , version 2 (24-02-2015)

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  • HAL Id : hal-01010967 , version 1

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Laurent Decreusefond, Matthias Schülte, Christoph Thäle. Functional Poisson approximation in Rubinstein distance. 2014. ⟨hal-01010967v1⟩
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