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Stochastic and integral geometry

Author: Rolf Schneider; Wolfgang Weil
Publisher: Berlin : Springer, ©2008.
Series: Probability and its applications (Springer-Verlag)
Edition/Format:   Print book : EnglishView all editions and formats
Database:WorldCat
Summary:
"Stochastic geometry has in recent years experienced considerable progress, both in its applications to other sciences and engineering, and in its theoretical foundations and mathematical expansion. This book, by two eminent specialists of the subject, provides a solid mathematical treatment of the basic models of stochastic geometry random sets, point processes of geometric objects (particles, flats), and random  Read more...
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Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: Rolf Schneider; Wolfgang Weil
ISBN: 9783540788584 3540788581 9783540788591 354078859X 3642097669 9783642097669
OCLC Number: 227033883
Description: xi, 693 pages ; 25 cm.
Contents: Foundations of Stochastic Geometry.- Prolog.- Random Closed Sets.- Point Processes.- Geometric Models.- Integral Geometry.- Averaging with Invariant Measures.- Extended Concepts of Integral Geometry.- Integral Geometric Transformations.- Selected Topics from Stochastic Geometry.- Some Geometric Probability Problems.- Mean Values for Random Sets.- Random Mosaics.- Non-stationary Models.- Facts from General Topology.- Invariant Measures.- Facts from Convex Geometry.
Series Title: Probability and its applications (Springer-Verlag)
Responsibility: Rolf Schneider, Wolfgang Weil.
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Abstract:

This book explores the basic stationary models used in stochastic geometry and the integral geometry needed for their investigation. It includes a chapter on selected problems about geometric  Read more...

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From the reviews: "In 'Stochastic and Integral Geometry,' R. Schneider and W. Weil give priority to the basic concepts in stochastic geometry ... while keeping from integral geometry only what is Read more...

 
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   schema:reviewBody ""Stochastic geometry has in recent years experienced considerable progress, both in its applications to other sciences and engineering, and in its theoretical foundations and mathematical expansion. This book, by two eminent specialists of the subject, provides a solid mathematical treatment of the basic models of stochastic geometry random sets, point processes of geometric objects (particles, flats), and random mosaics. It develops, in a measure-theoretic setting, the integral geometry for the motion, and the translation group, us needed for the investigation of these models under the usual invariance assumptions. A characteristic of the book is the interplay between stochastic and geometric arguments, leading to various major results. Its main theme, once the foundations have been laid, is the quantitative investigation of the basic models. This comprises the introduction of suitable parameters, in the form of functional densities, relations between them, and approaches to their estimation. Much additional information on stochastic geometry is collected in the section notes." "As a combination of probability theory and geometry, the volume is intended for readers from either field. Probabilists with interest in random spatial structures, or motivated by the prospect of applications, will find an in-depth presentation of the geometric background. Geometers can see integral geometry "at work" and may be surprised to learn how classical results from convex geometry have elegant applications in a stochastic setting."--Jacket." ;
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