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Stochastic Geometry and Its Applications.
An extensive update to a classic text Stochastic geometry and spatial statistics play a fundamental role in many modern branches of physics, materials sciences, engineering, biology and environmental sciences. They offer successful models for the description of random two- and three-dimensional micr...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Otros Autores: | , , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Hoboken :
Wiley,
2013.
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| Edición: | 3rd ed. |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Stochastic Geometry and its Applications; Contents; Foreword to the first edition; From the preface to the first edition; Preface to the second edition; Preface to the third edition; Notation; 1 Mathematical foundations; 1.1 Set theory; 1.2 Topology in Euclidean spaces; 1.3 Operations on subsets of Euclidean space; 1.4 Mathematical morphology and image analysis; 1.5 Euclidean isometries; 1.6 Convex sets in Euclidean spaces; 1.7 Functions describing convex sets; 1.7.1 General; 1.7.2 Set covariance; 1.7.3 Chord length distribution; 1.7.4 Erosion-dilation functions; 1.8 Polyconvex sets.
- 1.9 Measure and integration theory2 Point processes I
- The Poisson point process; 2.1 Introduction; 2.2 The binomial point process; 2.2.1 Introduction; 2.2.2 Basic properties; 2.2.3 Simulation; 2.3 The homogeneous Poisson point process; 2.3.1 Definition and defining properties; 2.3.2 Characterisation of the homogeneous Poisson point process; 2.3.3 Moments and moment measures; 2.3.4 The Palm distribution of a homogeneous Poisson point process; 2.4 The inhomogeneous and general Poisson point process; 2.5 Simulation of Poisson point processes.
- 2.5.1 Simulation of a homogeneous Poisson point process2.5.2 Simulation of an inhomogeneous Poisson point process; 2.6 Statistics for the homogeneous Poisson point process; 2.6.1 Introduction; 2.6.2 Estimating the intensity; 2.6.3 Testing the hypothesis of homogeneity; 2.6.4 Testing the Poisson process hypothesis; 3 Random closed sets I
- The Boolean model; 3.1 Introduction and basic properties; 3.1.1 Model description; 3.1.2 Applications; 3.1.3 Stationarity and isotropy; 3.1.4 Simulation; 3.1.5 The capacity functional; 3.1.6 Basic characteristics; 3.1.7 Contact distribution functions.
- 3.2 The Boolean model with convex grains3.2.1 The simplified formula for the capacity functional; 3.2.2 Intensities or densities of intrinsic volumes; 3.2.3 Contact distribution functions; 3.2.4 Morphological functions; 3.2.5 Intersections with linear subspaces; 3.2.6 Formulae for some special Boolean models with isotropic convex grains; 3.3 Coverage and connectivity; 3.3.1 Coverage probabilities; 3.3.2 Clumps; 3.3.3 Connectivity; 3.3.4 Percolation; 3.3.5 Vacant regions; 3.4 Statistics; 3.4.1 General remarks; 3.4.2 Testing model assumptions; 3.4.3 Estimation of model parameters.
- 3.5 Generalisations and variations3.6 Hints for practical applications; 4 Point processes II
- General theory; 4.1 Basic properties; 4.1.1 Introduction; 4.1.2 The distribution of a point process; 4.1.3 Notation; 4.1.4 Stationarity and isotropy; 4.1.5 Intensity measure and intensity; 4.1.6 Ergodicity and central limit theorem; 4.1.7 Contact distributions; 4.2 Marked point processes; 4.2.1 Fundamentals; 4.2.2 Intensity and mark distribution; 4.3 Moment measures and related quantities; 4.3.1 Moment measures; 4.3.2 Factorial moment measures; 4.3.3 Product densities; 4.3.4 The Campbell measure.