Stochastic Geometry and Its Applications

Sung Nok Chiu, Department of Mathematics, Hong Kong Baptist University, Hong KongDietrich Stoyan, Institute of Stochastics, TU Bergakademie Freiberg, GermanyWilfrid S. Kendall, Department of Statistics, University of Warwick, UKJoseph Mecke, Faculty of Mathematics and Computer Science, Friedrich-Schiller-Universität Jena, Germany

• Foreword to the first edition xiiiFrom the preface to the first edition xviiPreface to the second edition xixPreface to the third edition xxiNotation xxiii1 Mathematical foundations 11.1 Set theory 11.2 Topology in Euclidean spaces 31.3 Operations on subsets of Euclidean space 51.4 Mathematical morphology and image analysis 71.5 Euclidean isometries 91.6 Convex sets in Euclidean spaces 101.7 Functions describing convex sets 171.8 Polyconvex sets 241.9 Measure and integration theory 272 Point processes I: The Poisson point process 352.1 Introduction 352.2 The binomial point process 362.3 The homogeneous Poisson point process 412.4 The inhomogeneous and general Poisson point process 512.5 Simulation of Poisson point processes 532.6 Statistics for the homogeneous Poisson point process 553 Random closed sets I: The Boolean model 643.1 Introduction and basic properties 643.2 The Boolean model with convex grains 783.3 Coverage and connectivity 893.4 Statistics 953.5 Generalisations and variations 1033.6 Hints for practical applications 1064 Point processes II: General theory 1084.1 Basic properties 1084.2 Marked point processes 1164.3 Moment measures and related quantities 1204.4 Palm distributions 1274.5 The second moment measure 1394.6 Summary characteristics 1434.7 Introduction to statistics for stationary spatial point processes 1454.8 General point processes 1565 Point processes III: Models 1585.1 Operations on point processes 1585.2 Doubly stochastic Poisson processes (Cox processes) 1665.3 Neyman–Scott processes 1715.4 Hard-core point processes 1765.5 Gibbs point processes 1785.6 Shot-noise fields 2006 Random closed sets II: The general case 2056.1 Basic properties 2056.2 Random compact sets 2136.3 Characteristics for stationary and isotropic random closed sets 2166.4 Nonparametric statistics for stationary random closed sets 2306.5 Germ–grain models 2376.6 Other random closed set models 2556.7 Stochastic reconstruction of random sets 2767 Random measures 2797.1 Fundamentals 2797.2 Moment measures and related characteristics 2847.3 Examples of random measures 2868 Line, fibre and surface processes 2978.1 Introduction 2978.2 Flat processes 3028.3 Planar fibre processes 3148.4 Spatial fibre processes 3308.5 Surface processes 3338.6 Marked fibre and surface processes 3399 Random tessellations, geometrical networks and graphs 3439.1 Introduction and definitions 3439.2 Mathematical models for random tessellations 3469.3 General ideas and results for stationary planar tessellations 3579.4 Mean-value formulae for stationary spatial tessellations 3679.5 Poisson line and plane tessellations 3709.6 STIT tessellations 3759.7 Poisson-Voronoi and Delaunay tessellations 3769.8 Laguerre tessellations 3869.9 Johnson–Mehl tessellations 3889.10 Statistics for stationary tessellations 3909.11 Random geometrical networks 3979.12 Random graphs 40210 Stereology 41110.1 Introduction 41110.2 The fundamental mean-value formulae of stereology 41310.3 Stereological mean-value formulae for germ–grain models 42110.4 Stereological methods for spatial systems of balls 42510.5 Stereological problems for nonspherical grains (shape-and-size problems) 43610.6 Stereology for spatial tessellations 44010.7 Second-order characteristics and directional distributions 444References 453Author index 507Subject index 521