[Annotatie]: Stochastic Geometry is the mathematical discipline which studies mathematical models for random geometric structures. This book collects lectures presented at the CIME summer school in Martina Franca in September 2004. The main lecturers covered Spatial Statistics, Random Points, Integral Geometry and Random Sets. These are complemented by two additional contributions on Random Mosaics and Crystallization Processes. The book presents a comprehensive and up-to-date description of important aspects of Stochastic Geometry. [Inhoudsopgave]: Spatial Point Processes and their ApplicationsAdrian Baddeley1(76)1 Point Processes2(24)1.1 Point Processes in 1D and 2D2(1)1.2 Formulation of Point Processes3(3)1.3 Example: Binomial Process6(1)1.4 Foundations7(1)1.5 Poisson Processes8(4)1.6 Distributional Characterisation12(4)1.7 Transforming a Point Process16(3)1.8 Marked Point Processes19(2)1.9 Distances in Point Processes21(2)1.10 Estimation from Data23(1)1.11 Computer Exercises24(2)2 Moments and Summary Statistics26(16)2.1 Intensity26(4)2.2 Intensity for Marked Point Processes30(2)2.3 Second Moment Measures32(3)2.4 Second Moments for Stationary Processes35(3)2.5 The K-function38(1)2.6 Estimation from Data39(1)2.7 Exercises40(2)3 Conditioning42(15)3.1 Motivation42(2)3.2 Palm Distribution44(5)3.3 Palm Distribution for Stationary Processes49(2)3.4 Nearest Neighbour Function51(1)3.5 Conditional Intensity52(3)3.6 J-function55(1)3.7 Exercises56(1)4 Modelling and Statistical Inference57(16)4.1 Motivation57(1)4.2 Parametric Modelling and Inference58(3)4.3 Finite Point Processes61(1)4.4 Point Process Densities62(2)4.5 Conditional Intensity64(2)4.6 Finite Gibbs Models66(3)4.7 Parameter Estimation69(1)4.8 Estimating Equations70(2)<TABLE CELLSPACING=0 CELLPADDING=
nl
en