Theory of Random Sets

  • Ilya¬†Molchanov

Part of the Probability Theory and Stochastic Modelling book series (PTSM, volume 87)

Table of contents

  1. Front Matter
    Pages i-xvi
  2. Ilya Molchanov
    Pages 1-223
  3. Ilya Molchanov
    Pages 225-316
  4. Ilya Molchanov
    Pages 317-378
  5. Ilya Molchanov
    Pages 379-449
  6. Ilya Molchanov
    Pages 451-552
  7. Back Matter
    Pages 553-678

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.


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

Authors and affiliations

  • Ilya¬†Molchanov
    • 1
  1. 1.Institute of Mathematical Statistics and Actuarial ScienceUniversity of BernBernSwitzerland

Bibliographic information

  • DOI
  • Copyright Information Springer-Verlag London Ltd. 2017
  • Publisher Name Springer, London
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-1-4471-7347-2
  • Online ISBN 978-1-4471-7349-6
  • Series Print ISSN 2199-3130
  • Series Online ISSN 2199-3149
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