Read more
Informationen zum Autor Sung Nok Chiu , Department of Mathematics, Hong Kong Baptist University, Hong Kong Dietrich Stoyan , Institute of Stochastics, TU Bergakademie Freiberg, Germany Wilfrid S. Kendall , Department of Statistics, University of Warwick, UK Joseph Mecke , Faculty of Mathematics and Computer Science, Friedrich-Schiller-Universität Jena, Germany Klappentext An extensive update to a classic textStochastic 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 micro and macro structures and statistical methods for their analysis.The previous edition of this book has served as the key reference in its field for over 18 years and is regarded as the best treatment of the subject of stochastic geometry, both as a subject with vital applications to spatial statistics and as a very interesting field of mathematics in its own right.This edition:* Presents a wealth of models for spatial patterns and related statistical methods.* Provides a great survey of the modern theory of random tessellations, including many new models that became tractable only in the last few years.* Includes new sections on random networks and random graphs to review the recent ever growing interest in these areas.* Provides an excellent introduction to theory and modelling of point processes, which covers some very latest developments.* Illustrate the forefront theory of random sets, with many applications.* Adds new results to the discussion of fibre and surface processes.* Offers an updated collection of useful stereological methods.* Includes 700 new references.* Is written in an accessible style enabling non-mathematicians to benefit from this book.* Provides a companion website hosting information on recent developments in the field www.wiley.com/go/cskmStochastic Geometry and its Applications is ideally suited for researchers in physics, materials science, biology and ecological sciences as well as mathematicians and statisticians. It should also serve as a valuable introduction to the subject for students of mathematics and statistics. Zusammenfassung 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. Inhaltsverzeichnis Foreword to the first edition xiii From the preface to the first edition xvii Preface to the second edition xix Preface to the third edition xxi Notation xxiii 1 Mathematical foundations 1 1.1 Set theory 1 1.2 Topology in Euclidean spaces 3 1.3 Operations on subsets of Euclidean space 5 1.4 Mathematical morphology and image analysis 7 1.5 Euclidean isometries 9 1.6 Convex sets in Euclidean spaces 10 1.7 Functions describing convex sets 17 1.8 Polyconvex sets 24 1.9 Measure and integration theory 27 2 Point processes I: The Poisson point process 35 2.1 Introduction 35 2.2 The binomial point process 36 2.3 The homogeneous Poisson point process 41 2.4 The inhomogeneous and general Poisson point process 51 2.5 Simulation of Poisson point processes 53 2.6 Statistics for the homogeneous Poisson point process 55 3 Random closed sets I: The Boolean model 64 3.1 Introduction and basic properties 64 3.2 The Boolean model with convex grains 78 3.3 Coverage and connectivity 89 3.4 Statistics 95 3.5 Generalisations and variations 103 3.6 Hints for practical applications 106 4 Point processes II: General theory 108 4.1 Basic properties 108
