Factorization Calculus and Geometric Probability (Encyclopedia of Mathematics and its Applications, Vol. 33) - Hardcover

Ambartzumian, R. V.

Hardcover

ISBN 10: 0521345359 ISBN 13: 9780521345354

Publisher: Cambridge University Press, 1990

Synopsis

The classical subjects of geometric probability and integral geometry, and the more modern one of stochastic geometry, are developed here in a novel way to provide a framework in which they can be studied. The author focuses on factorization properties of measures and probabilities implied by the assumption of their invariance with respect to a group, in order to investigate nontrivial factors. The study of these properties is the central theme of the book. Basic facts about integral geometry and random point process theory are developed in a simple geometric way, so that the whole approach is suitable for a nonspecialist audience. Even in the later chapters, where the factorization principles are applied to geometrical processes, the only prerequisites are standard courses on probability and analysis. The main ideas presented have application to such areas as stereology and geometrical statistics and this book will be a useful reference book for university students studying probability theory and stochastic geometry, and research mathematicians interested in this area.

About this title

Book Description

This unique book develops the classical subjects of geometric probability and integral geometry, and the more modern one of stochastic geometry, in rather a novel way to provide a unifying framework in which they can be studied. The author focuses on factorisation properties of measures and probabilities implied by the assumption of their invariance with respect to a group, in order to investigate non-trivial factors.

Review

"The book is written in the characteristic style of the author, full of new and interesting ideas and, although in appearance the prerequisites are only standard courses on analysis and probability, it is not easy to read. It must be carefully thought out in many of its details, but the effort is well compensated by the great deal of information and new ways of thinking it supplies." L. A. Santaló, Mathematical Reviews

"The author of the present book, R.V. Ambartzumian, is one of the leading experts in the mentioned fields. He has influenced the development of integral and stochastic geometry by numerous, interesting results, new methods, and problems, a great part of which is presented in the monograph....highly recommended to mathematicians interested in integral and stochastic geometry. It is very stimulating because of the abundance of interesting results, models, and problems." J. Mecke, SIAM Review

Edition details

• Publisher: Cambridge University Press
• Publication date: 1990
• Language: English
• ISBN 10: 0521345359
• ISBN 13: 9780521345354
• Binding: Hardcover
• Edition number: 1
• Number of pages: 300