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.
