Theory of Random Sets
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
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Ilya Molchanov
Theory of Random Sets Second Edition
Probability Theory and Stochastic Modelling Volume 87 Editors-in-chief Peter W. Glynn, Stanford, CA, USA Andreas E. Kyprianou, Bath, UK Yves Le Jan, Orsay, France Advisory Board Søren Asmussen, Aarhus, Denmark Martin Hairer, Coventry, UK Peter Jagers, Gothenburg, Sweden Ioannis Karatzas, New York, NY, USA Frank P. Kelly, Cambridge, UK Bernt Øksendal, Oslo, Norway George Papanicolaou, Stanford, CA, USA Etienne Pardoux, Marseille, France Edwin Perkins, Vancouver, Canada Halil Mete Soner, Zürich, Switzerland
The Probability Theory and Stochastic Modelling series is a merger and continuation of Springer’s two well established series Stochastic Modelling and Applied Probability and Probability and Its Applications series. It publishes research monographs that make a significant contribution to probability theory or an applications domain in which advanced probability methods are fundamental. Books in this series are expected to follow rigorous mathematical standards, while also displaying the expository quality necessary to make them useful and accessible to advanced students as well as researchers. The series covers all aspects of modern probability theory including • • • • • •
Gaussian processes Markov processes Random fields, point processes and random sets Random matrices Statistical mechanics and random media Stochastic analysis
as well as applications that include (but are not restricted to): • Branching processes and other models of population growth • Communications and processing networks • Computational methods in probability and stochastic processes, including simulation • Genetics and other stochastic models in biology and the life sciences • Information theory, signal processing, and image synthesis • Mathematical economics and finance • Statistical methods (e.g. empirical processes, MCMC) • Statistics for stochastic processes • Stochastic control • Stochastic models in operations research and stochastic optimization • Stochastic models in the physical sciences More information about this series at http://www.springer.com/series/13205
Ilya Molchanov
Theory of Random Sets Second Edition
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Ilya Molchanov Institute of Mathematical Statistics and Actuarial Science University of Bern Bern, Switzerland
ISSN 2199-3130 ISSN 2199-3149 (electronic) Probability Theory and Stochastic Modelling ISBN 978-1-4471-7347-2 ISBN 978-1-4471-7349-6 (eBook) DOI 10.1007/978-1-4471-7349-6 Library of Congress Control Number: 2017949364 Mathematics Subject Classification (2010): Primary: 60D05; Secondary: 26E25, 28B20, 52A22, 49J53, 54C65, 60B05, 60E07, 60F15, 60G55, 60G57, 62M30 Originally published in the series: Probability and Its Applications © Springer-Verlag London Ltd. 2005, 2017 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical
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