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Erschienen in:
Stochastic Analysis for Poisson Processes Kapitel lesen Erstes Kapitel lesen

2016 | OriginalPaper | Buchkapitel

Introduction to Stochastic Geometry

verfasst von : Daniel Hug, Matthias Reitzner

Erschienen in: Stochastic Analysis for Poisson Point Processes

Verlag: Springer International Publishing

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Abstract

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.

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Vorheriges Kapitel Malliavin Calculus for Stochastic Processes and Random Measures with Independent Increments
Nächstes Kapitel The Malliavin–Stein Method on the Poisson Space
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Metadaten
Titel
Introduction to Stochastic Geometry
verfasst von
Daniel Hug
Matthias Reitzner
Copyright-Jahr
2016
Buch
Stochastic Analysis for Poisson Point Processes

Print ISBN: 978-3-319-05232-8

Electronic ISBN: 978-3-319-05233-5

Copyright-Jahr: 2016

DOI
https://doi.org/10.1007/978-3-319-05233-5_5