New Perspectives in Stochastic Geometry

by Kendall, Wilfrid S.; Molchanov, Ilya

• ISBN13: 9780199232574
• ISBN10: 0199232571
• Format: Hardcover
• Copyright: 2010-02-01
• Publisher: Oxford University Press

Summary

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. Ithas 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 randomizedallocation 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 otherareas 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 fromthe coverage of a wide and rapidly developing field.

Author Biography

W.S.Kendall earned a DPhil in probability theory at the University of Oxford in 1979, and then worked as a Lecturer and then Senior Lecturer in Statistics at Hull and Strathclyde Universities before coming to Warwick in 1988. He has authored or edited 5 books and published about 90 papers. At Warwick he has risen through the ranks from Lecturer to Reader to Professor, serving as Departmental Chair and now as co-Director of the innovative national Academy for PhD Training in Statistics. Other service has included acting as founding coordinating editor of the Stochastic Geometry and Statistical Applications section of the Advances in Applied Probability journal, as chief editor of Electronic Communications in Probability, as Scientific Secretary of the Bernoulli Society, and as Programme Chair for the Bernoulli/IMS World Congress, Barcelona 2004. His research interests lie in the interfaces between probability, geometry, and computing.
I.Molchanov received his Ph.D. degree in mathematics from Kiev University (Ukraine) in 1987 and his Habilitation from TU Bergakademie Freiberg (Germany) in 1994. Between 1987 and 1992 he was an Assistant Professor at Kiev Technological Institute. From 1992 to 1994 he has been working at TU Bergakademie Freiberg as an Alexander von Humboldt Research Fellow. Then he took over a research position at Centrum voor Wiskunde en Informatica (CWI), Amsterdam. In December 1995 he joined the Department of Statistics of the University of Glasgow (Scotland) where he became Professor in Applied Probability in 1998. From 2002 he holds a chair in Probability Theory in the University of Bern. He has authored 3 books and published about 90 papers. His research interests are concentrated around random sets and their applications in probability, finance, statistics and image analysis.

Table of Contents

Preface

Classical stochastic geometry

New Developments In Classical Stochastic Geometry

Random polytopes

Modern random measures: Palm theory and related models

Limit theorems in stochastic geometry

Tessellations

Stochastic Geometry And Modern Probability

Percolation and random graphs

Random directed and on-line networks

Random fractals

Statistics And Stochastic Geometry

Inference

Statistical shape theory

Set estimation

Data depth: multivariate statistics and geometry

Applications

Applications of stochastic geometry in image analysis

Stereology

Physics of spatially structured materials

Stochastic geometry and telecommunications networks

Random sets in finance and econometrics

Index

Table of Contents provided by Publisher. All Rights Reserved.