Stochastic geometry and its applications
 Uniform Title
 Stochastische Geometrie. English
 Author/Creator
 Stoyan, Dietrich.
 Language
 English.
 Edition
 Third edition / Sung Nok Chiu, Dietrich Stoyan, Wilfrid S. Kendall, Joseph Mecke.
 Publication
 Chichester, West Sussex, United Kingdom : John Wiley & Sons Inc., 2013.
 Physical description
 xxvi, 544 pages : illustrations ; 25 cm.
 Series
 Wiley series in probability and statistics.
Access
Available online

Stacks

Unknown
QA273.5 .S7813 2013

Unknown
QA273.5 .S7813 2013
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Contributors
 Contributor
 Chiu, Sung Nok.
 Kendall, W. S.
 Mecke, Joseph.
Contents/Summary
 Bibliography
 Includes bibliographical references (pages [453]505) and indexes.
 Contents

 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 4.2 Marked point processes 116 4.3 Moment measures and related quantities 120 4.4 Palm distributions 127 4.5 The second moment measure 139 4.6 Summary characteristics 143 4.7 Introduction to statistics for stationary spatial point processes 145 4.8 General point processes 156 5 Point processes III: Models 158 5.1 Operations on point processes 158 5.2 Doubly stochastic Poisson processes (Cox processes) 166 5.3 NeymanScott processes 171 5.4 Hardcore point processes 176 5.5 Gibbs point processes 178 5.6 Shotnoise fields 200 6 Random closed sets II: The general case 205 6.1 Basic properties 205 6.2 Random compact sets 213 6.3 Characteristics for stationary and isotropic random closed sets 216 6.4 Nonparametric statistics for stationary random closed sets 230 6.5 Germgrain models 237 6.6 Other random closed set models 255 6.7 Stochastic reconstruction of random sets 276 7 Random measures 279 7.1 Fundamentals 279 7.2 Moment measures and related characteristics 284 7.3 Examples of random measures 286 8 Line, fibre and surface processes 297 8.1 Introduction 297 8.2 Flat processes 302 8.3 Planar fibre processes 314 8.4 Spatial fibre processes 330 8.5 Surface processes 333 8.6 Marked fibre and surface processes 339 9 Random tessellations, geometrical networks and graphs 343 9.1 Introduction and definitions 343 9.2 Mathematical models for random tessellations 346 9.3 General ideas and results for stationary planar tessellations 357 9.4 Meanvalue formulae for stationary spatial tessellations 367 9.5 Poisson line and plane tessellations 370 9.6 STIT tessellations 375 9.7 PoissonVoronoi and Delaunay tessellations 376 9.8 Laguerre tessellations 386 9.9 JohnsonMehl tessellations 388 9.10 Statistics for stationary tessellations 390 9.11 Random geometrical networks 397 9.12 Random graphs 402 10 Stereology 411 10.1 Introduction 411 10.2 The fundamental meanvalue formulae of stereology 413 10.3 Stereological meanvalue formulae for germgrain models 421 10.4 Stereological methods for spatial systems of balls 425 10.5 Stereological problems for nonspherical grains (shapeandsize problems) 436 10.6 Stereology for spatial tessellations 440 10.7 Secondorder characteristics and directional distributions 444 References 453 Author index 507 Subject index 521.
 (source: Nielsen Book Data)
 Publisher's Summary
 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 threedimensional 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 editi on : 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 nonmathematicians to benefit from this book. Provides a companion website hosting information on recent developments in the field www.wiley.com/go/cskm Stochastic 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.
(source: Nielsen Book Data)  Supplemental links
 Cover image
Subjects
 Subject
 Stochastic geometry.
Bibliographic information
 Publication date
 2013
 Series
 Wiley series in probability and statistics
 Note
 Revision of: Stochastic geometry and its applications / Dietrich Stoyan, Wilfrid S. Kendall, Joseph Mecke.  2nd ed.  ©1995.
 ISBN
 0470664819
 9780470664810