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Theory of Random Sets [electronic resource] /by Ilya Molchanov.

by Molchanov, Ilya [author.]; SpringerLink (Online service).
Material type: materialTypeLabelBookSeries: Probability and Its Applications: Publisher: London : Springer London, 2005.Description: XVI, 488 p. 33 illus. online resource.ISBN: 9781846281501.Subject(s): Mathematics | Distribution (Probability theory) | Mathematical physics | Statistics | Economics | Mathematics | Probability Theory and Stochastic Processes | Game Theory, Economics, Social and Behav. Sciences | Mathematical and Computational Physics | Statistics for Engineering, Physics, Computer Science, Chemistry & Geosciences | Electronic and Computer Engineering | Economic TheoryDDC classification: 519.2 Online resources: Click here to access online
Contents:
Random Closed Sets and Capacity Functionals -- Expectations of Random Sets -- Minkowski Addition -- Unions of Random Sets -- Random Sets and Random Functions. Appendices: Topological Spaces -- Linear Spaces -- Space of Closed Sets -- Compact Sets and the Hausdorff Metric -- Multifunctions and Continuity -- Measures and Probabilities -- Capacities -- Convex Sets -- Semigroups and Harmonic Analysis -- Regular Variation. References -- List of Notation -- Name Index -- Subject Index.
In: Springer eBooksSummary: 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.
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Long Loan MAIN LIBRARY
QA273.A1-274.9 (Browse shelf) Available

Random Closed Sets and Capacity Functionals -- Expectations of Random Sets -- Minkowski Addition -- Unions of Random Sets -- Random Sets and Random Functions. Appendices: Topological Spaces -- Linear Spaces -- Space of Closed Sets -- Compact Sets and the Hausdorff Metric -- Multifunctions and Continuity -- Measures and Probabilities -- Capacities -- Convex Sets -- Semigroups and Harmonic Analysis -- Regular Variation. References -- List of Notation -- Name Index -- Subject Index.

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.

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