Factorization Calculus and Geometric Probability

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Overview

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.
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Editorial Reviews

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"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

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Product Details

Table of Contents

Preface; 1. Cavalieri principle and other prerequisites; 2. Measures invariant with respect to translations; 3. Measures invariant with respect to Euclidean motions; 4. Haar measures on groups of affine transformations; 5. Combinatorial integral geometry; 6. Basic integrals; 7. Stochastic point processes; 8. Palm distributions of point processes; 9. Poisson-generated geometrical processes; 10. Section through planar geometrical processes; References; Index.

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