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Stochastic disorder problems / Albert N. Shiryaev ; [translated from the Russian by Andrei Iacob ; foreword by H. Vincent Poor].

Shiryaev, Albert N.; Poor, H. Vincent.; Iacob, Andrei.
2019
QA274.2 .S55 2019
Available Online
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Title
Stochastic disorder problems / Albert N. Shiryaev ; [translated from the Russian by Andrei Iacob ; foreword by H. Vincent Poor].
Author
Shiryaev, Albert N.
ISBN
9783030015268 (electronic book)
3030015262 (electronic book)
3030015254
9783030015251
DOI
https://doi.org/10.1007/978-3-030-01526-8
Published
Cham : Springer, 2019.
Language
English
Description
1 online resource (412 pages)
Item Number
10.1007/978-3-030-01526-8 doi
Call Number
QA274.2 .S55 2019
Dewey Decimal Classification
519.2/2
Summary
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.
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Access limited to authorized users.
Source of Description
Description based on online resource; title from digital title page (viewed on April 04, 2019).
Added Author
Poor, H. Vincent.
Iacob, Andrei.
Series
Probability theory and stochastic modelling ; v. 93.
Available in Other Form
Print version: 9783030015251
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Preface
Introduction
Probabilistic-Statistical Models in Quickest Detection Problems. Discrete and Continuous Time
Basic Settings and Solutions of Quickest Detection Problems. Discrete Time
Optimal Stopping Times. General Theory for the Discrete-Time Case
Optimal Stopping Rules. General Theory for the Discrete-Time Case in the Markov Representation
Optimal Stopping Rules. General Theory for the Continuous-Time Case
Basic Formulations and Solutions of Quickest Detection Problems. Continuous-Time. Models with Brownian motion
Multi-Stage Quickest Detection of Breakdown of a Stationary Regime. Model with Brownian Motion
Disorder on Filtered Probability Spaces
Bayesian and Variational Problems of Hypothesis Testing. Brownian Motion Models
Applications to Financial Mathematics
References
Term Index
Notation Index.

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