Overview
- 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
Part of the book series: Probability Theory and Stochastic Modelling (PTSM, volume 87)
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Table of contents (5 chapters)
Keywords
- 60D05, 26E25, 28B20, 52A22, 49J53, 54C65, 60B05, 60E07, 60F15
- 60G55, 60G57, 62M30
- random closed sets
- selections of random sets
- capacity functional
- set-valued process
- set-valued martingales
- non-additive measures
- partially identified models
- partially identified econometric models
- transaction costs in finance
- selection expectation random sets
- Minkowski sums
- unions of random sets
About this book
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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Bibliographic Information
Book Title: Theory of Random Sets
Authors: Ilya Molchanov
Series Title: Probability Theory and Stochastic Modelling
DOI: https://doi.org/10.1007/978-1-4471-7349-6
Publisher: Springer London
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag London Ltd. 2017
Hardcover ISBN: 978-1-4471-7347-2Published: 29 December 2017
Softcover ISBN: 978-1-4471-7407-3Published: 09 September 2018
eBook ISBN: 978-1-4471-7349-6Published: 14 December 2017
Series ISSN: 2199-3130
Series E-ISSN: 2199-3149
Edition Number: 2
Number of Pages: XVI, 678
Number of Illustrations: 26 b/w illustrations
Additional Information: Originally published in the series: Probability and Its Applications
Topics: Probability Theory and Stochastic Processes, Game Theory, Economics, Social and Behav. Sciences, Theoretical, Mathematical and Computational Physics, Statistics for Engineering, Physics, Computer Science, Chemistry and Earth Sciences, Electrical Engineering, Economic Theory/Quantitative Economics/Mathematical Methods