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Stochastic Disorder Problems

  • Albert N. Shiryaev
Book

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

About this book

Introduction

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.

Keywords

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

Authors and affiliations

  • Albert N. Shiryaev
    • 1
  1. 1.Steklov Mathematical InstituteRussian Academy of SciencesMoscowRussia

Bibliographic information

  • 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