Theory of Random Sets / Edition 1

Theory of Random Sets / Edition 1

by Ilya Molchanov
     
 

ISBN-10: 185233892X

ISBN-13: 9781852338923

Pub. Date: 04/14/2005

Publisher: Springer London

"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…  See more details below

Overview

"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." 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:
9781852338923
Publisher:
Springer London
Publication date:
04/14/2005
Series:
Probability and Its Applications Series
Edition description:
2005
Pages:
488
Product dimensions:
6.10(w) x 9.25(h) x 0.24(d)

Table of Contents

1Random closed sets and capacity functionals1
2Expectations of random sets145
3Minkowski addition195
4Unions of random sets241
5Random sets and random functions303
App. ATopological spaces and linear spaces387
App. BSpace of closed sets398
App. CCompact sets and the Hausdorff metric402
App. DMultifunctions and semicontinuity409
App. EMeasures, probabilities and capacities412
App. FConvex sets421
App. GSemigroups and harmonic analysis425
App. HRegular variation428

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