Stochastic and Integral Geometry (Probability and Its Applications) - Softcover

Schneider, Rolf; Weil, Wolfgang

Softcover

ISBN 10: 3642097669 ISBN 13: 9783642097669

Publisher: Springer, 2010

Synopsis

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 probabilities and an outlook to non-stationary models.

About this title

Review:

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 relevant for applications in stochastic geometry. ... Each chapter section is concluded by notes in which the main references are cited and numerous possible extensions are discussed. ... Stochastic and Integral Geometry is a profound work by two eminent specialists which is essential reading for those willing to learn deep theory.” (Pierre Calka, Mathematical Geosciences, Vol. 45, 2013)

“This book ... provides the systematic and exhaustive account of mathematical foundations of stochastic geometry with particular emphasis on tools from convex geometry. ... The thorough and up-to-date presentation in this text makes it an invaluable source for researchers pursuing studies not only in stochastic geometry, but also in convex geometry and various applications ... . an absolutely indispensable part of all mathematical libraries. ... also beneficial for personal collections of all mathematicians who ever deal with probability measures on spaces of geometric objects.” (Ilya S. Molchanov, Zentralblatt MATH, Vol. 1175, 2010)

“The book presents a number of results that are otherwise scattered among an immense number of research papers and mostly provides full proofs for them. ... The most remarkable aspect of the book is the reader-friendly structure and the style in which it has been written. The book is also worth owning not only for those working in stochastic geometry and immediately related fields of theoretical and applied probability and spatial statistics. ... This book ... will be an essential part of every mathematical library.” (V. K. Oganyan, Mathematical Reviews, Issue 2010 g)

From the Back Cover:

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.

About this edition

• Publisher: Springer
• Publication date: 2010
• ISBN 10: 3642097669
• ISBN 13: 9783642097669
• Binding: Paperback
• Number of pages: 706