Theory of Random Sets - Softcover

Molchanov, Ilya

Softcover

ISBN 10: 1848008023 ISBN 13: 9781848008021

Publisher: Springer, 2008

Synopsis

This is the first systematic exposition of random sets theory since Matheron (1975), with full proofs, exhaustive bibliographies and literature notes

Interdisciplinary connections and applications of random sets are emphasized throughout the book

An extensive bibliography in the book is available on the Web at http://liinwww.ira.uka.de/bibliography/math/random.closed.sets.html, and is accompanied by a search engine

About this title

Review

From the reviews:

"Together with the foundations of the modern probability theory Kolmogorov introduced the concept of a random set. ... The book is written in a theorem-proof style, where the proofs are quite detailed and clearly presented. ... to enable easier reading, the author provides visual illustrations where necessary. ... the author provides a vast bibliography on the subject, which is completely searchable on author’s website. The book should be read and even more studied by any researcher or a student considering research in this field." (Ita Cirovic Donev, MathDL, January, 2006)

"This book is part of the Springer-Verlag series ‘Probability and its applications’. ... The most remarkable aspect of the book is the reader-friendly structure and the style in which it has been written. There are masses of examples either worked out in the book or left for the reader. A number of facts are equipped with graphical illustrations. This book has a good index and index of notations, and a very detailed bibliography ... . It will be an essential part of every mathematical library." (V. K. Oganyan, Mathematical Reviews, Issue 2006 b)

"The book under review develops ... an approach in a self-contained and systematic manner. Full proofs are given, and many steps are illustrated by graphs and drawings. The interdisciplinary nature of the theory of random sets within mathematics is well shown. ... The book will be an invaluable reference for probabilists, mathematicians, statisticians and electronic and electrical engineers in the fields of image analysis. ... The book is highly recommended both for personal use and for libraries." (Janos Galambos, Zentralblatt MATH, Vol. 1109 (11), 2007)

"Random sets play an important role in many applications of mathematics ... . This book is an important contribution to the mathematical theory and will surely serve as a valuable textbook for students as well as researchers. It presents a self-contained survey of all the significant results ... . A number of open problems are presented and each chapter concludes with a list of bibliographical notes." (EMS Newsletter, September, 2007)

From the Back Cover

Stochastic geometry is a relatively new branch of mathematics. Although its predecessors such as geometric probability date back to the 18th century, the formal concept of a random set was developed in the beginning of the 1970s. Theory of Random Sets presents a state of the art treatment of the modern theory, but it does not neglect to recall and build on the foundations laid by Matheron and others, including the vast advances in stochastic geometry, probability theory, set-valued analysis, and statistical inference of the 1990s.

The book is entirely self-contained, systematic and exhaustive, with the full proofs that are necessary to gain insight. It shows the various interdisciplinary relationships of random set theory within other parts of mathematics, and at the same time, fixes terminology and notation that are often varying in the current literature to establish it as a natural part of modern probability theory, and to provide a platform for future development. An extensive, searchable bibliography to accompany the book is freely available via the web.

The book will be an invaluable reference for probabilists, mathematicians in convex and integral geometry, set-valued analysis, capacity and potential theory, mathematical statisticians in spatial statistics and image analysis, specialists in mathematical economics, and electronic and electrical engineers interested in image analysis.

Edition details

• Publisher: Springer
• Publication date: 2008
• Language: English
• ISBN 10: 1848008023
• ISBN 13: 9781848008021
• Binding: Paperback
• Number of pages: 508