Stochastic Geometry, Spatial Statistics and Random Fields

1. Front Matter

   Pages i-xxiv

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2. Stein’s Method for Approximating Complex Distributions, with a View towards Point Processes

   • Dominic Schuhmacher

   Pages 1-30

3. Clustering Comparison of Point Processes, with Applications to Random Geometric Models

   • Bartłomiej Błaszczyszyn, Dhandapani Yogeshwaran

   Pages 31-71

4. Random Tessellations and their Application to the Modelling of Cellular Materials

   • Claudia Redenbach, André Liebscher

   Pages 73-93

5. Stochastic 3D Models for the Micro-structure of Advanced Functional Materials

   • Volker Schmidt, Gerd Gaiselmann, Ole Stenzel

   Pages 95-141

6. Boolean Random Functions

   • Dominique Jeulin

   Pages 143-169

7. Random Marked Sets and Dimension Reduction

   • Viktor Beneš, Jakub Stanĕk, Blažena Kratochvílová, Ondřej Šedivý

   Pages 171-203

8. Space-Time Models in Stochastic Geometry

   • Viktor Beneš, Michaela Prokešová, Kateřina Staňková Helisová, Markéta Zikmundová

   Pages 205-232

9. Rotational Integral Geometry and Local Stereology - with a View to Image Analysis

   • Eva B. Vedel Jensen, Allan Rasmusson

   Pages 233-255

10. An Introduction to Functional Data Analysis

    • Ulrich Stadtmüller, Marta Zampiceni

    Pages 257-292

11. Some Statistical Methods in Genetics

    • Alexander Bulinski

    Pages 293-320

12. Extrapolation of Stationary Random Fields

    • Evgeny Spodarev, Elena Shmileva, Stefan Roth

    Pages 321-368

13. Spatial Process Simulation

    • Dirk P. Kroese, Zdravko I. Botev

    Pages 369-404

14. Introduction to Coupling-from-the-Past using R

    • Wilfrid S. Kendall

    Pages 405-439

15. Back Matter

    Pages 441-466

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This volume is an attempt to provide a graduate level introduction to various aspects of stochastic geometry, spatial statistics and random fields, with special emphasis placed on fundamental classes of models and algorithms as well as on their applications, e.g. in materials science, biology and genetics. This book has a strong focus on simulations and includes extensive codes in Matlab and R which are widely used in the mathematical community. It can be seen as a continuation of the recent volume 2068 of Lecture Notes in Mathematics, where other issues of stochastic geometry, spatial statistics and random fields were considered with a focus on asymptotic methods.

• 60D05,60G55,60G60,62H11,62M40,62P30,62P10.
• Mathematical Models
• Random Fields
• Simulation Algorithms
• Spatial Statistics
• Stochastic Geometry

• Institute of Stochastic, Ulm University, Ulm, Germany

  Volker Schmidt

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