Theory of Random Sets
Autor: | Ilya Molchanov |
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EAN: | 9781447173496 |
eBook Format: | |
Sprache: | Englisch |
Produktart: | eBook |
Veröffentlichungsdatum: | 14.12.2017 |
Kategorie: | |
Schlagworte: | 26E25 28B20 49J53 52A22 54C65 60B05 60D05 60E07 60F15 60G55 60G57 62M30 capacity functional non-additive measures pa partially identified models random closed sets selections of random sets set-valued martingales set-valued process |
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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.
Ilya Molchanov is Professor of Probability Theory at the Department of Mathematical Statistics and Actuarial Science at the University of Bern, Switzerland.