Stochastic and Integral Geometry

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Springer Science & Business Media, Sep 8, 2008 - Mathematics - 694 pages

Stochastic geometry deals with models for random geometric structures. Its early beginnings are found in playful geometric probability questions, and it has vigorously developed during recent decades, when an increasing number of real-world applications in various sciences required solid mathematical foundations. Integral geometry studies geometric mean values with respect to invariant measures and is, therefore, the appropriate tool for the investigation of random geometric structures that exhibit invariance under translations or motions. Stochastic and Integral Geometry provides the mathematically oriented reader with a rigorous and detailed introduction to the basic stationary models used in stochastic geometry – random sets, point processes, random mosaics – and to the integral geometry that is needed for their investigation. The interplay between both disciplines is demonstrated by various fundamental results. A chapter on selected problems about geometric probabilities and an outlook to non-stationary models are included, and much additional information is given in the section notes.

 

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Contents

Prolog
1
Random Closed Sets 17
15
Point Processes
47
Geometric Models
99
Averaging with Invariant Measures 167
165
Extended Concepts of Integral Geometry
211
Integral Geometric Transformations 265
264
Some Geometric Probability Problems 293
291
Nonstationary Models
521
Facts from General Topology 559
558
Invariant Measures
575
Facts from Convex Geometry
597
References
637
Author Index 675
674
Subject Index
681
Notation Index
689

Mean Values for Random Sets
377
Random Mosaics
445

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About the author (2008)

Rolf Schneider: Born 1940, Studies of Mathematics and Physics in Frankfurt/M, Diploma 1964, PhD 1967 (Frankfurt), Habilitation 1969 (Bochum), 1970 Professor TU Berlin, 1974 Professor Univ. Freiburg, 2003 Dr. h.c. Univ. Salzburg, 2005 Emeritus

Wolfgang Weil: Born 1945, Studies of Mathematics and Physics in Frankfurt/M, Diploma 1968, PhD 1971 (Frankfurt), Habilitation 1976 (Freiburg), 1978 Akademischer Rat Univ. Freiburg, 1980 Professor Univ. Karlsruhe

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