SET RECONSTRUCTION BY VORONOI CELLS
| Autor(en): | Reitzner, M. Spodarev, E. Zaporozhets, D. |
Stichwörter: | Mathematics; perimeter; Poisson point process; Poisson-Voronoi cell; Poisson-Voronoi tessellation; Statistics & Probability | Erscheinungsdatum: | 2012 | Herausgeber: | APPLIED PROBABILITY TRUST | Journal: | ADVANCES IN APPLIED PROBABILITY | Volumen: | 44 | Ausgabe: | 4 | Startseite: | 938 | Seitenende: | 953 | Zusammenfassung: | For a Borel set A and a homogeneous Poisson point process eta in R-d of intensity lambda > 0, define the Poisson-Voronoi approximation A(eta) of A as a union of all Voronoi cells with nuclei from eta lying in A. If A has a finite volume and perimeter, we find an exact asymptotic of EVol(A Delta A(eta)) as lambda -> infinity, where Vol is the Lebesgue measure. Estimates for all moments of Vol(A(eta)) and Vol(A Delta A(eta)) together with their asymptotics for large lambda are obtained as well. |
ISSN: | 00018678 |
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