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New Perspectives in Stochastic Geometry
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New Perspectives in Stochastic Geometry

Wilfrid S. Kendall and Ilya Molchanov

Abstract

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 sch ... More

Keywords: stochastic geometry, random patterns, probability theory, statistics, image analysis, material science, fractals, percolation theory, randomized allocation

Bibliographic Information

Print publication date: 2009 Print ISBN-13: 9780199232574
Published to Oxford Scholarship Online: February 2010 DOI:10.1093/acprof:oso/9780199232574.001.0001

Authors

Affiliations are at time of print publication.

Wilfrid S. Kendall, editor
Department of Statistics, University of Warwick, UK

Ilya Molchanov, editor
Department of Mathematical Statistics and Actuarial Science, University of Bern, Switzerland

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Contents

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1 Classical Stochastic Geometry

Rolf Schneider and Wolfgang Weil

Part I New Developments in Classical Stochastic Geometry

2 Random Polytopes

Matthias Reitzner

5 Tessellations

Pierre Calka

PART II Stochastic Geometry And Modern Probability

6 Percolation and Random Graphs

Remco van der Hofstad

7 Random Directed and on‐Line Networks

Mathew D. Penrose and Andrew R. Wade

8 Random Fractals

Peter Mörters

Part III Statistics and Stochastic Geometry

9 Inference

Jesper Møller

10 Statistical Shape Theory

Wilfrid S. Kendall and Huiling Le

11 Set Estimation

Antonio Cuevas and Ricardo Fraiman

Part IV Applications

14 Stereology

Werner Nagel

End Matter