Theory of Random Sets / Edition 1

Theory of Random Sets / Edition 1

by Ilya Molchanov
     
 

Shastic 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

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Overview

Shastic 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 shastic 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.

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Product Details

ISBN-13:
9781849969499
Publisher:
Springer London
Publication date:
12/14/2011
Series:
Probability and Its Applications Series
Edition description:
Softcover reprint of hardcover 1st ed. 2005
Pages:
488
Product dimensions:
6.14(w) x 9.21(h) x 1.02(d)

Table of Contents

Random Closed Sets and Capacity Functionals.- Expectations of Random Sets.- Minkowski Addition.- Unions of Random Sets.- Random Sets and Random Functions.

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