Stochastic Disorder Problems

Albert N Shiryaev author Andrei Iacob translator

Format:Hardback

Publisher:Springer Nature Switzerland AG

Published:20th Mar '19

Currently unavailable, and unfortunately no date known when it will be back

Stochastic Disorder Problems cover

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,whichoften 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.

“Researchers and graduate students interested in optimal stopping, decision theory, and statistical sequential analysis will find this book useful. It is a very welcome addition to the literature of these fields.” (Rick Durrett, MAA Reviews, December 14, 2019)

ISBN: 9783030015251

Dimensions: unknown

Weight: unknown

397 pages

1st ed. 2019