Wilfrid S. Kendall - Böcker

Stochastic Geometry is a subject with roots stretching back at least 300 years, but one which has only been formed as an academic area in the last 50 years. It covers the study of random patterns, their probability theory, and the challenging problems raised by their statistical analysis. It has grown rapidly in response to challenges in all kinds of applied science, from image analysis through to materials science. Recently, still more stimulus has arisen from exciting new links with rapidly developing areas of mathematics, from fractals through percolation theory to randomized allocation schemes. Coupled with many ongoing developments arising from all sorts of applications, the area is changing and developing rapidly. This book is intended to lay foundations for future research directions, by collecting together 17 chapters contributed by leading researchers in the field, both theoreticians and people involved in applications, surveying these new developments both in theory and in applications. It will introduce and lay foundations for appreciating the fresh perspectives, new ideas and interdisciplinary connections now arising from Stochastic Geometry and from other areas of mathematics now connecting to this area. This will benefit young researchers wishing to gain quick access to the area, scientists from other fields wanting perspectives on what the area has to offer their own speciality, and workers already active in the field who will enjoy and profit from the coverage of a wide and rapidly developing field.

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/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.