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Field name	Details
Dewey Class	519.2
Title	Stochastic and Integral Geometry ([Ebook]) / by Rolf Schneider, Wolfgang Weil.
Author	Schneider, Rolf , 1940-
Added Personal Name	Weil, Wolfgang
Other name(s)	SpringerLink (Online service)
Publication	Berlin, Heidelberg : Springer , 2008.
Physical Details	: online resource.
Series	Probability and Its Applications 1431-7028
ISBN	9783540788591
Summary Note	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, as 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.:
Contents note	1.Prologue -- Part I: Foundations of Stochastic Geometry -- 2.Random Closed Sets -- 3.Point Processes -- 4.Geometric Models -- Part II: Integral Geometry -- 5.Averaging with Invariant Measures -- 6.Extended Concepts of Integral Geometry -- 7.Integral-geometric Transformations -- Part III: Selected Topics from Stochastic Geometry -- 8.Some Geometric Probability Problems -- 9.Mean Values for Random Sets -- 10.Random Mosaics -- 11.Non-stationary Models -- Part IV: Appendix -- 12.Facts from General Topology -- 13.Invariant Measures -- 14.Facts from Convex Geometry -- References -- Index.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users).
Internet Site	http://dx.doi.org/10.1007/978-3-540-78859-1
Links to Related Works	Subject References: Convex and Discrete Geometry . Discrete groups . Distribution (Probability theory) . Mathematics . Probability theory and stochastic processes . Authors: author . Schneider, Rolf 1940- . Weil, Wolfgang . Corporate Authors: SpringerLink (Online service) . Series: Probability and Its Applications . Classification: 519.2 . 519.23 (DDC 22) .

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Stochastic and Integral Geometry

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