# Stochastic Disorder Problems

Part of the Probability Theory and Stochastic Modelling book series (PTSM, volume 93)

Advertisement

Book

Part of the Probability Theory and Stochastic Modelling book series (PTSM, volume 93)

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.

93-XX, 60G40, 62Cxx, 62L10, 62L15, 91A60, 91B06 dynamical analysis of statistical data stochastic disorder problems quickest detection problems discrete and continuous time optimal stopping times optimal stopping rules formulations of quickest detection problems basic settings of quickest detection problems solutions of quickest detection problems Disorder on Filtered Probability Spaces Brownian Motion Multi-Stage Quickest Detection Breakdown of a Stationary Regime

- DOI https://doi.org/10.1007/978-3-030-01526-8
- Copyright Information Springer Nature Switzerland AG 2019
- Publisher Name Springer, Cham
- eBook Packages Mathematics and Statistics
- Print ISBN 978-3-030-01525-1
- Online ISBN 978-3-030-01526-8
- Series Print ISSN 2199-3130
- Series Online ISSN 2199-3149
- Buy this book on publisher's site

- Industry Sectors
- Finance, Business & Banking
- Electronics
- Engineering