Stochastic and Integral Geometry

  • Rolf Schneider
  • Wolfgang Weil

Part of the Probability and Its Applications book series (PIA)

Table of contents

  1. Front Matter
    Pages I-XI
  2. Foundations of Stochastic Geometry

    1. Pages 1-13
    2. Pages 17-46
    3. Pages 47-98
    4. Pages 99-163
  3. Integral Geometry

  4. Selected Topics from Stochastic Geometry

  5. Appendix

  6. Back Matter
    Pages 637-693

About this book

Introduction

Stochastic geometry has in recent years experienced considerable progress, both in its applications to other sciences and engineering, and in its theoretical foundations and mathematical expansion. This book, by two eminent specialists of the subject, provides a solid mathematical treatment of the basic models of stochastic geometry -- random sets, point processes of geometric objects (particles, flats), and random mosaics. It develops, in a measure-theoretic setting, the integral geometry for the motion and the translation group, as needed for the investigation of these models under the usual invariance assumptions. A characteristic of the book is the interplay between stochastic and geometric arguments, leading to various major results. Its main theme, once the foundations have been laid, is the quantitative investigation of the basic models. This comprises the introduction of suitable parameters, in the form of functional densities, relations between them, and approaches to their estimation. Much additional information on stochastic geometry is collected in the section notes.

As a combination of probability theory and geometry, the volume is intended for readers from either field. Probabilists with interest in random spatial structures, or motivated by the prospect of applications, will find an in-depth presentation of the geometric background. Geometers can see integral geometry "at work" and may be surprised to learn how classical results from convex geometry have elegant applications in a stochastic setting.

Keywords

Geometric probability Integral geometry Random set Stochastic geometry Variance point process

Authors and affiliations

  • Rolf Schneider
    • 1
  • Wolfgang Weil
    • 2
  1. 1.Mathematisches InstitutAlbert-Ludwigs-UniversitätFreiburgGermany
  2. 2.Institut für Algebra und GeometrieUniversität KarlsruheKarlsruheGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-540-78859-1
  • Copyright Information Springer-Verlag Berlin Heidelberg 2008
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-540-78858-4
  • Online ISBN 978-3-540-78859-1
  • Series Print ISSN 1431-7028
  • About this book