POISSON-VORONOI APPROXIMATION
成果类型：
Article
署名作者：
Heveling, Matthias; Reitzner, Matthias
署名单位：
Technische Universitat Wien
刊物名称：
ANNALS OF APPLIED PROBABILITY
ISSN/ISSBN：
1050-5164
DOI：
10.1214/08-AAP561
发表日期：
2009
页码：
719-736
关键词：
摘要：
Let X be a Poisson point process and K subset of R(d) a measurable set. Construct the Voronoi cells of all points x is an element of X with respect to X, and denote by v(X)(K) the union of all Voronoi cells with nucleus in K. For K a compact convex set the expectation of the volume difference V(v(X)(K)) - V(K) and the symmetric difference V(v(X)(K)Delta K) is computed. Precise estimates for the variance of both quantities are obtained which follow from a new jackknife inequality for the variance of functionals of a Poisson point process. Concentration inequalities for both quantities are proved using Azuma's inequality.
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