
New Perspectives in Stochastic Geometry
Oxford University Press
Published on 26. November 2009
Book
Hardback
606 pages
978-0-19-923257-4 (ISBN)
Description
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.
Reviews / Votes
This well written volume is a long awaited welcome, especially for a novice who desires to enter this fast growing interdisciplinary area, and a must have reference for researchers in the field. * Libertas Mathematica *More details
Language
English
Place of publication
Oxford
United Kingdom
Target group
College/higher education
Illustrations
40 illustrations
Dimensions
Height: 241 mm
Width: 162 mm
Thickness: 40 mm
Weight
1036 gr
ISBN-13
978-0-19-923257-4 (9780199232574)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Persons
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.
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.
Editor
Department of Statistics, University of Warwick, UK
Department of Mathematical Statistics and Actuarial Science, University of Bern, Switzerland
Content
Preface ; 1. Classical stochastic geometry ; I NEW DEVELOPMENTS IN CLASSICAL STOCHASTIC GEOMETRY ; 2. Random polytopes ; 3. Modern random measures: Palm theory and related models ; 4. Limit theorems in stochastic geometry ; 5. Tessellations ; II STOCHASTIC GEOMETRY AND MODERN PROBABILITY ; 6. Percolation and random graphs ; 7. Random directed and on-line networks ; 8. Random fractals ; III STATISTICS AND STOCHASTIC GEOMETRY ; 9. Inference ; 10. Statistical shape theory ; 11. Set estimation ; 12. Data depth: multivariate statistics and geometry ; IV APPLICATIONS ; 13. Applications of stochastic geometry in image analysis ; 14. Stereology ; 15. Physics of spatially structured materials ; 16. Stochastic geometry and telecommunications networks ; 17. Random sets in finance and econometrics ; Index