New Perspectives in Stochastic Geometry

Kendall, Wilfrid S. (EDT)/ Molchanov, Ilya (EDT)

Oxford University Press（2009/11発売）

• 製本 Hardcover:ハードカバー版／ページ数 606 p.
• 言語 ENG
• 商品コード 9780199232574
• DDC分類 519.2

Full 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.

Contents

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