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Stochastic Disorder Problems
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(Buch) |
Dieser Artikel gilt, aufgrund seiner Grösse, beim Versand als 3 Artikel!
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| 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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