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Stochastic Geometry, Spatial Statistics and Random Fields

Asymptotic Methods

  • Book
  • © 2013

Overview

Editors:
  1. Evgeny Spodarev

    1. Ulm, Germany

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  • Comprises introductory material as well as advances topics with a significant number of proofs
  • Numerous images ease the understanding of complex mathematical notions
  • Includes a large number of excercises for active reading Provides vast research bibliography
  • Includes supplementary material: sn.pub/extras

Part of the book series: Lecture Notes in Mathematics (LNM, volume 2068)

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Table of contents (12 chapters)

  1. Front Matter

    Pages i-xxiv
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  2. Foundations of Stochastic Geometry and Theory of Random Sets

    • Ilya Molchanov
    Pages 1-20

  3. Introduction into Integral Geometry and Stereology

    • Markus Kiderlen
    Pages 21-48

  4. Spatial Point Patterns: Models and Statistics

    • Adrian Baddeley
    Pages 49-114

  5. Asymptotic Methods in Statistics of Random Point Processes

    • Lothar Heinrich
    Pages 115-150

  6. Random Tessellations and Cox Processes

    • Florian Voss, Catherine Gloaguen, Volker Schmidt
    Pages 151-182

  7. Asymptotic Methods for Random Tessellations

    • Pierre Calka
    Pages 183-204

  8. Random Polytopes

    • Daniel Hug
    Pages 205-238

  9. Limit Theorems in Discrete Stochastic Geometry

    • Joseph Yukich
    Pages 239-275

  10. Introduction to Random Fields

    • Alexander Bulinski, Evgeny Spodarev
    Pages 277-335

  11. Central Limit Theorems for Weakly Dependent Random Fields

    • Alexander Bulinski, Evgeny Spodarev
    Pages 337-383

  12. Strong Limit Theorems for Increments of Random Fields

    • Ulrich Stadtmüller
    Pages 385-398

  13. Geometry of Large Random Trees: SPDE Approximation

    • Yuri Bakhtin
    Pages 399-420

  14. Back Matter

    Pages 421-448
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Keywords

About this book

This volume provides a modern introduction to stochastic geometry, random fields and spatial statistics at a (post)graduate level. It is focused on asymptotic methods in geometric probability including weak and strong limit theorems for random spatial structures (point processes, sets, graphs, fields) with applications to statistics. Written as a contributed volume of lecture notes, it will be useful not only for students but also for lecturers and researchers interested in geometric probability and related subjects.

Editors and Affiliations

  • Ulm, Germany

    Evgeny Spodarev

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