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Theory of random sets

Molchanov, Ilya.

Theory of random sets

Record Type:	Electronic resources : Monograph/item
Title/Author:	Theory of random setsby Ilya Molchanov.
Author:	Molchanov, Ilya.
Published:	London :Springer London :2017.
Description:	xvi, 678 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
Subject:	Random sets.
Online resource:	http://dx.doi.org/10.1007/978-1-4471-7349-6
ISBN:	9781447173496$q(electronic bk.)

Theory of random sets
Molchanov, Ilya.

Theory of random sets[electronic resource] /by Ilya Molchanov. - 2nd ed. - London :Springer London :2017. - xvi, 678 p. :ill., digital ;24 cm. - Probability theory and stochastic modelling,v.872199-3130 ;. - Probability theory and stochastic modelling ;v.70..

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.

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.

ISBN: 9781447173496$q(electronic bk.)

Standard No.: 10.1007/978-1-4471-7349-6doiSubjects--Topical Terms:

234837
Random sets.

LC Class. No.: QA273.5 / .M656 2017

Dewey Class. No.: 519.2

Theory of random sets
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505 0 $a 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.
520 $a 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.
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