Ilya Molchanov: Theory of Random Sets | Buch

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Cover: 9781447173472 | Theory of Random Sets | Ilya Molchanov | Buch | Englisch | 2017

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Sprache: Englisch

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Beschreibung

This monograph, now in a thoroughly revised second edition, offers the latest research on random sets. It has been extended to include substantial developments achieved since 2005, some of them motivated by applications of random sets to econometrics and finance.
The present volume builds on the foundations laid by Matheron and others, including the vast advances in stochastic geometry, probability theory, set-valued analysis, and statistical inference. 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 often vary in the literature, establishing it as a natural part of modern probability theory and providing a platform for future development. It is completely self-contained, systematic and exhaustive, with the full proofs that are necessary to gain insight.
Aimed at research level, Theory of Random Sets will be an invaluable reference for probabilists; mathematicians working in convex and integral geometry, set-valued analysis, capacity and potential theory; mathematical statisticians in spatial statistics and uncertainty quantification; specialists in mathematical economics, econometrics, decision theory, and mathematical finance; and electronic and electrical engineers interested in image analysis.

Über den Autor

Ilya Molchanov is Professor of Probability Theory at the Department of Mathematical Statistics and Actuarial Science at the University of Bern, Switzerland.

Zusammenfassung

Comprehensively covers the theory of random sets

Explores interdisciplinary connections and applications of the theory

Extensive and updated bibliography

Includes latest developments in the field

Inhaltsverzeichnis

1 Random Closed Sets and Capacity Functionals.- 2 Expectations of Random Sets.- 3 Minkowski Sums.- 4 Unions of Random Sets.- 5 Random Sets and Random Functions.- A Topological spaces and metric spaces.- B Linear spaces.- C Space of closed sets.- D Compact sets and the Hausdorff metric.- E Multifunctions and semicontinuity.- F Measures and probabilities.- G Capacities.- H Convex sets.- I Semigroups, cones, and harmonic analysis.- J Regular variation.- References.

Details

Erscheinungsjahr:	2017
Fachbereich:	Wahrscheinlichkeitstheorie
Genre:	Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Buch
Seiten:	696
Reihe:	Probability Theory and Stochastic Modelling
Inhalt:	xvi 678 S. 26 s/w Illustr. 678 p. 26 illus.
ISBN-13:	9781447173472
ISBN-10:	1447173473
Sprache:	Englisch
Herstellernummer:	978-1-4471-7347-2
Ausstattung / Beilage:	HC runder Rücken kaschiert
Einband:	Gebunden
Autor:	Molchanov, Ilya
Auflage:	2nd ed. 2017
Hersteller:	Springer London Springer-Verlag London Ltd. Probability Theory and Stochastic Modelling
Maße:	241 x 160 x 41 mm
Von/Mit:	Ilya Molchanov
Erscheinungsdatum:	29.12.2017
Gewicht:	1,324 kg

preigu-id: 110975022