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) |
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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: |
05 Dec 2022 15:01 |
Publisher DOI: |
10.1214/15-AOP1020 |
BORIS DOI: |
10.7892/boris.93224 |
URI: |
https://boris.unibe.ch/id/eprint/93224 |
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