Introduction to Stochastic Geometry
- Daniel HugAffiliated withDepartment of Mathematics, Karlsruhe Institute of Technology
- , Matthias ReitznerAffiliated withInstitut für Mathematik, Universität Osnabrück Email author
This chapter introduces some of the fundamental notions from stochastic geometry. Background information from convex geometry is provided as far as this is required for the applications to stochastic geometry.
First, the necessary definitions and concepts related to geometric point processes and from convex geometry are provided. These include Grassmann spaces and invariant measures, Hausdorff distance, parallel sets and intrinsic volumes, mixed volumes, area measures, geometric inequalities and their stability improvements. All these notions and related results will be used repeatedly in the present and in the subsequent chapters of the book.
Second, a variety of important models and problems from stochastic geometry will be reviewed. Among these are the Boolean model, random geometric graphs, intersection processes of (Poisson) processes of affine subspaces, random mosaics, and random polytopes. We state the most natural problems and point out important new results and directions of current research.
- Introduction to Stochastic Geometry
- Book Title
- Stochastic Analysis for Poisson Point Processes
- Book Subtitle
- Malliavin Calculus, Wiener-Itô Chaos Expansions and Stochastic Geometry
- pp 145-184
- Print ISBN
- Online ISBN
- Series Title
- Bocconi & Springer Series
- Series Volume
- Series Subtitle
- Mathematics, Statistics, Finance and Economics
- Series ISSN
- Springer International Publishing
- Copyright Holder
- Springer International Publishing Switzerland
- Additional Links
- Industry Sectors
- eBook Packages
- Editor Affiliations
- 7. Unité de Recherche en Mathématiques, Université du Luxembourg
- 8. Institut für Mathematik, Osnabrück University
- Author Affiliations
- 9. Department of Mathematics, Karlsruhe Institute of Technology, 76128, Karlsruhe, Germany
- 10. Institut für Mathematik, Universität Osnabrück, Albrechtstraße 28a, 49086, Osnabrück, Germany
To view the rest of this content please follow the download PDF link above.