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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 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.
Cited literature [45 references]
https://hal.archives-ouvertes.fr/hal-01010967
Contributor : Laurent Decreusefond Connect 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
Contributor : Laurent Decreusefond Connect 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
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