Stochastic Geometry and Its Applications

Front Cover
John Wiley & Sons, Jun 27, 2013 - Mathematics - 584 pages

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 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/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.

 

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Contents

Notation
Mathematical Foundations
Random Closed Sets ll The General Case
Random Closed Sets I The Boolean Model
Point Processes ll General Theory
Point Processes Ill Models
Random Measures
Line Fibre and Surface Processes
Random Tessellations Geometrical Networks
Tessellations
Stereology
References
Author Index
Copyright

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About the author (2013)

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-Universitšt Jena, Germany

Bibliographic information