Probability Theory and Stochastic Modelling

Stochastic Disorder Problems

Authors: Shiryaev, Albert N.

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  • Provides the theory and methods to solve stochastic quickest detection tasks in disorder problems
  • Shows that most quickest detection problems can be reformulated as optimal stopping problems
  • Examines both the discrete-time and continuous-time cases
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  • ISBN 978-3-030-01526-8
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About this book

This monograph focuses on those stochastic quickest detection tasks in disorder problems that arise in the dynamical analysis of statistical data. These include quickest detection of randomly appearing targets, of spontaneously arising effects, and of arbitrage (in financial mathematics). There is also currently great interest in quickest detection methods for randomly occurring intrusions in information systems and in the design of defense methods against cyber-attacks. The author shows that the majority of quickest detection problems can be reformulated as optimal stopping problems where the stopping time is the moment the occurrence of disorder is signaled. Thus, considerable attention is devoted to the general theory of optimal stopping rules, and to its concrete problem-solving methods.

The exposition covers both the discrete time case, which is in principle relatively simple and allows step-by-step considerations, and the continuous-time case, which often requires more technical machinery such as martingales, supermartingales, and stochastic integrals. There is a focus on the well-developed apparatus of Brownian motion, which enables the exact solution of many problems. The last chapter presents applications to financial markets.

Researchers and graduate students interested in probability, decision theory and statistical sequential analysis will find this book useful.

About the authors

Albert N. Shiryaev is Chief Scientific Researcher and Professor of Probability Theory and Mathematical Statistics at the Steklov Mathematical Institute of the Russian Academy of Sciences and Head of the Department of Probability Theory in the Mechanics and Mathematics Faculty at Lomonosov Moscow State University. He is the author of several books, including Problems in Probability  [translated by Andrew Lyasov], Optimal Stopping Rules [translated by A.B. Aries], and Statistics of Random Processes [with Robert S. Liptser]. He was the recipient of the A.A.MarkovPrize in 1974, of the A.N.Kolmogorov Prize in 1994, and of the Golden P.L.Chebyshev Medal of the Russian Academy of Science in 2017.


Table of contents (10 chapters)

Table of contents (10 chapters)
  • Probabilistic-Statistical Models in Quickest Detection Problems. Discrete and Continuous Time

    Pages 1-12

    Shiryaev, Albert N.

  • Basic Settings and Solutions of Quickest Detection Problems. Discrete Time

    Pages 13-56

    Shiryaev, Albert N.

  • Optimal Stopping Times. General Theory for the Discrete-Time Case

    Pages 57-73

    Shiryaev, Albert N.

  • Optimal Stopping Rules. General Theory for the Discrete-Time Case in the Markov Representation

    Pages 75-91

    Shiryaev, Albert N.

  • Optimal Stopping Rules. General Theory for the Continuous-Time Case

    Pages 93-137

    Shiryaev, Albert N.

Buy this book

eBook $89.00
price for USA (gross)
  • ISBN 978-3-030-01526-8
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $119.99
price for USA
  • ISBN 978-3-030-01525-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.

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Bibliographic Information

Bibliographic Information
Book Title
Stochastic Disorder Problems
Authors
Translated by
Iacob, A.
Series Title
Probability Theory and Stochastic Modelling
Series Volume
93
Copyright
2019
Publisher
Springer International Publishing
Copyright Holder
Springer Nature Switzerland AG
eBook ISBN
978-3-030-01526-8
DOI
10.1007/978-3-030-01526-8
Hardcover ISBN
978-3-030-01525-1
Series ISSN
2199-3130
Edition Number
1
Number of Pages
XIX, 397
Number of Illustrations
27 b/w illustrations
Topics