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Stochastic Disorder Problems

Autor: Albert N. Shiryaev, Andrei Iacob

Jazyk:

Vazba: Pevná

Vydavatel: Springer Nature Switzerland AG

Dostupnost: Skladem u dodavatele

Odesíláme za 10-13 dnů

2 970 Kč

This monograph focuses on those stochastic quickest detection tasks in disorder problems that arise...

Informace o knize

Autor

Albert N. Shiryaev, Andrei Iacob

Jazyk

Angličtina

Vazba

Kniha - Pevná

Vydáno

2019

Stránek

397

EAN

9783030015251

Enbook ID

20124458

Vydavatel

Springer Nature Switzerland AG

Hmotnost

793

Rozměry

155 x 235 x 29

Kompletní popis

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.