Asymptotic theory for statistics of the Poisson--Voronoi approximation
Abstract
This paper establishes expectation and variance asymptotics for statistics of the Poisson--Voronoi approximation of general sets, as the underlying intensity of the Poisson point process tends to infinity. Statistics of interest include volume, surface area, Hausdorff measure, and the number of faces of lower-dimensional skeletons. We also consider the complexity of the so-called Voronoi zone and the iterated Voronoi approximation. Our results are consequences of general limit theorems proved with an abstract Steiner-type formula applicable in the setting of sums of stabilizing functionals.
Cite
@article{arxiv.1503.08963,
title = {Asymptotic theory for statistics of the Poisson--Voronoi approximation},
author = {Christoph Thäle and J. E. Yukich},
journal= {arXiv preprint arXiv:1503.08963},
year = {2016}
}
Comments
Published at http://dx.doi.org/10.3150/15-BEJ732 in the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm)