scientific article

zbMath0964.52009MaRDI QIDQ3835848

Rolf Schneider, Wolfgang Weil

Publication date: 29 November 1999

Title: zbMATH Open Web Interface contents unavailable due to conflicting licenses.

zbMATH Keywords

estimationstochastic geometrystereologyPalm distributionMinkowski functionalintegral geometryPoisson processBoolean modelrandom tessellationkinematic formulaconvex geometryChoquet capacityrandom closed setassociated zonoidCrofton formulafunctional densityergodic and mixing properties(marked) point processgerm-grain-model (process)

Mathematics Subject Classification ID

Random fields (60G60) Inference from stochastic processes and prediction (62M20) Random fields; image analysis (62M40) Applications of statistics to biology and medical sciences; meta analysis (62P10) Geometric probability and stochastic geometry (60D05) Applications of statistics in engineering and industry; control charts (62P30) Introductory exposition (textbooks, tutorial papers, etc.) pertaining to probability theory (60-01) Inequalities and extremum problems involving convexity in convex geometry (52A40) Applications of statistics to physics (62P35) Random measures (60G57) Convexity and finite-dimensional Banach spaces (including special norms, zonoids, etc.) (aspects of convex geometry) (52A21) Convex sets in (n) dimensions (including convex hypersurfaces) (52A20) Point processes (e.g., Poisson, Cox, Hawkes processes) (60G55) Random convex sets and integral geometry (aspects of convex geometry) (52A22) Introductory exposition (textbooks, tutorial papers, etc.) pertaining to convex and discrete geometry (52-01)

Related Items

On support measures in Minkowski spaces and contact distributions in stochastic geometry., The limit shape of the zero cell in a stationary Poisson hyperplane tessellation., Unnamed Item, The -Delaunay tessellation: Description of the model and geometry of typical cells, Sectional Voronoi tessellations: characterization and high-dimensional limits, The $\beta$-Delaunay tessellation III: Kendall's problem and limit theorems in high dimensions, Fitting of random tessellation models to keratin filament networks, Unnamed Item, Faces of Poisson-Voronoi mosaics, Random Laguerre tessellations, Estimation of the mean normal measure from flat sections, The iteration of random tessellations and a construction of a homogeneous process of cell divisions, On the Boolean model of Wiener sausages, Stationary partitions and Palm probabilities, On the estimation of intrinsic volume densities of stationary random closed sets, Limit theorems for functionals on the facets of stationary random tessellations, Stationary flows and uniqueness of invariant measures, Absolute continuity for curvature measures of convex sets. III, Large Poisson-Voronoi cells and Crofton cells, Polynomial parallel volume, convexity and contact distributions of random sets, Intersection densities of nonstationary Poisson processes of hypersurfaces, Limit theorems for stationary tessellations with random inner cell structures, Convergence of algorithms for reconstructing convex bodies and directional measures, On weak stationarity and weak isotropy of processes of convex bodies and cylinders, Expectation of random polytopes, Central limit theorems for Poisson hyperplane tessellations, Stationary iterated tessellations, Crack STIT tessellations: characterization of stationary random tessellations stable with respect to iteration, Central limit theorems for functionals of stationary germ-grain models, Poisson-Voronoi approximation, The mean width of the oloid and integral geometric applications of it, Estimation of the directional measure of planar random sets by digitization, Spectral theory for random closed sets and estimating the covariance via frequency space, Central limit theorems for random polytopes, The surface pair correlation function for stationary Boolean models, Some distributional results for Poisson-Voronoi tessellations