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

Decreusefond, Laurent; Schulte, Matthias; Thäle, Christoph (2016). Functional Poisson approximation in Kantorovich-Rubinstein distance with applications to U-statistics and stochastic geometry. The annals of probality, 44(3), pp. 2147-2197. Institute of Mathematical Statistics 10.1214/15-AOP1020

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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.

Item Type:

Journal Article (Original Article)

Division/Institute:

08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematical Statistics and Actuarial Science

UniBE Contributor:

Schulte, Matthias

Subjects:

500 Science > 510 Mathematics

ISSN:

0091-1798

Publisher:

Institute of Mathematical Statistics

Language:

English

Submitter:

David Ginsbourger

Date Deposited:

25 Apr 2017 17:33

Last Modified:

25 Apr 2017 17:33

Publisher DOI:

10.1214/15-AOP1020

BORIS DOI:

10.7892/boris.93224

URI:

https://boris.unibe.ch/id/eprint/93224

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