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.
Citation
Laurent Decreusefond. Matthias Schulte. Christoph Thäle. "Functional Poisson approximation in Kantorovich–Rubinstein distance with applications to U-statistics and stochastic geometry." Ann. Probab. 44 (3) 2147 - 2197, May 2016. https://doi.org/10.1214/15-AOP1020
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