Researchers and graduate students interested in probability, decision theory and statistical sequential analysis will find this book useful. The last chapter presents applications to financial markets. There is a focus on the well-developed apparatus of Brownian motion, which enables the exact solution of many problems. Shiryaev, On martingale methods in the boundary crossing problems for Brownian motion, Sovrem. 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. Shiryaev, On solution of the optimal stopping problem for processes with independent increments, Stochastics, 79:3-4 (2007), 393406 (cited: 17) (cited: 26) 63. Thus, considerable attention is devoted to the general theory of optimal stopping rules, and to its concrete problem-solving methods. 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. 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. These include quickest detection of randomly appearing targets, of spontaneously arising effects, and of arbitrage (in financial mathematics). This monograph focuses on those stochastic quickest detection tasks in disorder problems that arise in the dynamical analysis of statistical data.
0 kommentar(er)
