# U-Statistics in Stochastic Geometry

@article{LachezeRey2015UStatisticsIS,
title={U-Statistics in Stochastic Geometry},
author={Raphael Lacheze-Rey and Matthias Reitzner},
journal={arXiv: Probability},
year={2015},
volume={7},
pages={229-253}
}
• Published 28 February 2015
• Mathematics
• arXiv: Probability
A U-statistic of order k with kernel $$f: \mathbb{X}^{k} \rightarrow \mathbb{R}^{d}$$ over a Poisson process η is defined as $$\displaystyle{\sum _{(x_{1},\ldots,x_{k})}f(x_{1},\ldots,x_{k}),}$$ where the summation is over k-tuples of distinct points of η, under appropriate integrability assumptions on f. U-statistics play an important role in stochastic geometry since many interesting functionals can be written as U-statistics, like intrinsic volumes of intersection processes…
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