Editors:
- A self-contained introduction to essential topics in stochastic geometry and infinite-dimensional stochastic analysis
- Provides a unique and systematic discussion of Malliavin calculus in the framework of stochastic geometry
- Includes detailed discussion of applications, e.g. to telecommunication networks, or to statistical problems on homogeneous spaces
- Includes supplementary material: sn.pub/extras
Part of the book series: Bocconi & Springer Series (BS, volume 7)
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Table of contents (10 chapters)
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Front Matter
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Back Matter
About this book
Stochastic geometry is the branch of mathematics that studies geometric structures associated with random configurations, such as random graphs, tilings and mosaics. Due to its close ties with stereology and spatial statistics, the results in this area are relevant for a large number of important applications, e.g. to the mathematical modeling and statistical analysis of telecommunication networks, geostatistics and image analysis. In recent years – due mainly to the impetus of the authors and their collaborators – a powerful connection has been established between stochastic geometry and the Malliavin calculus of variations, which is a collection of probabilistic techniques based on the properties of infinite-dimensional differential operators. This has led in particular to the discovery of a large number of new quantitative limit theorems for high-dimensional geometric objects.
This unique book presents an organic collection of authoritative surveys written bythe principal actors in this rapidly evolving field, offering a rigorous yet lively presentation of its many facets.
Reviews
Editors and Affiliations
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Unité de Recherche en Mathématiques, Université du Luxembourg, Luxembourg, Luxembourg
Giovanni Peccati
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Institut für Mathematik, Osnabrück University, Osnabrück, Germany
Matthias Reitzner
Bibliographic Information
Book Title: Stochastic Analysis for Poisson Point Processes
Book Subtitle: Malliavin Calculus, Wiener-Itô Chaos Expansions and Stochastic Geometry
Editors: Giovanni Peccati, Matthias Reitzner
Series Title: Bocconi & Springer Series
DOI: https://doi.org/10.1007/978-3-319-05233-5
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing Switzerland 2016
Hardcover ISBN: 978-3-319-05232-8Published: 19 July 2016
Softcover ISBN: 978-3-319-79147-0Published: 30 May 2018
eBook ISBN: 978-3-319-05233-5Published: 07 July 2016
Series ISSN: 2039-1471
Series E-ISSN: 2039-148X
Edition Number: 1
Number of Pages: XV, 346
Number of Illustrations: 2 illustrations in colour
Topics: Probability Theory and Stochastic Processes, Combinatorics, Polytopes, Applications of Mathematics