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Stochastic Analysis for Poisson Point Processes

Malliavin Calculus, Wiener-Itô Chaos Expansions and Stochastic Geometry

  • Giovanni Peccati
  • Matthias Reitzner

Part of the Bocconi & Springer Series book series (BS, volume 7)

Table of contents

  1. Front Matter
    Pages i-xv
  2. Ilya Molchanov, Sergei Zuyev
    Pages 81-101
  3. Daniel Hug, Matthias Reitzner
    Pages 145-184
  4. Solesne Bourguin, Giovanni Peccati
    Pages 185-228
  5. Raphaël Lachièze-Rey, Matthias Reitzner
    Pages 229-253
  6. Matthias Schulte, Christoph Thäle
    Pages 255-294
  7. Solesne Bourguin, Claudio Durastanti, Domenico Marinucci, Giovanni Peccati
    Pages 295-310
  8. Laurent Decreusefond, Ian Flint, Nicolas Privault, Giovanni Luca Torrisi
    Pages 311-342
  9. Back Matter
    Pages 343-346

About this book

Introduction

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 by the principal actors in this rapidly evolving field, offering a rigorous yet lively presentation of its many facets.

Keywords

Stochastic geometry Stochastic analysis Point processes Limit theorems Malliavin calculus

Editors and affiliations

  • Giovanni Peccati
    • 1
  • Matthias Reitzner
    • 2
  1. 1.Unité de Recherche en MathématiquesUniversité du LuxembourgLuxembourgLuxembourg
  2. 2.Institut für MathematikOsnabrück UniversityOsnabrückGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-05233-5
  • Copyright Information Springer International Publishing Switzerland 2016
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-05232-8
  • Online ISBN 978-3-319-05233-5
  • Series Print ISSN 2039-1471
  • Series Online ISSN 2039-148X
  • Buy this book on publisher's site