rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: Stochastic Disorder Problems
  name:
    name part: Shiryaev, Albert N.
    role:
      role term: creator
    role:
      role term: author.
    role:
      role term: aut
    role:
      role term: http://id.loc.gov/vocabulary/relators/aut
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: gw
    date issued: 2019
    edition: 1st ed. 2019.
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: XIX, 397 p. 27 illus. online resource.
  abstract: 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.
  table of contents: Preface -- Introduction -- Probabilistic-Statistical Models in Quickest Detection Problems. Discrete and Continuous Time -- Basic Settings and Solutions of Quickest Detection Problems. Discrete Time -- Optimal Stopping Times. General Theory for the Discrete-Time Case -- Optimal Stopping Rules. General Theory for the Discrete-Time Case in the Markov Representation -- Optimal Stopping Rules. General Theory for the Continuous-Time Case -- Basic Formulations and Solutions of Quickest Detection Problems. Continuous-Time. Models with Brownian motion -- Multi-Stage Quickest Detection of Breakdown of a Stationary Regime. Model with Brownian Motion -- Disorder on Filtered Probability Spaces -- Bayesian and Variational Problems of Hypothesis Testing. Brownian Motion Models -- Applications to Financial Mathematics -- References -- Term Index -- Notation Index.
  note: by Albert N. Shiryaev.
  subject:
    topic: System theory
  subject:
    topic: Probabilities
  subject:
    topic: Statistics
  subject:
    topic: Economics, Mathematical
  subject:
    topic: Finance-Mathematics
  subject:
    topic: Systems Theory, Control
  subject:
    topic: Probability Theory and Stochastic Processes
  subject:
    topic: Statistical Theory and Methods
  subject:
    topic: Quantitative Finance
  subject:
    topic: Financial Mathematics
  subject:
    topic: Bayesian Inference
  classification: Q295
  classification: QA402.3-402.37
  classification: 519
  related item:
    title info:
      title: Springer eBooks
  related item:
    title info:
      title: Probability Theory and Stochastic Modelling, 93
  identifier: 9783030015268
  identifier: https://doi.org/10.1007/978-3-030-01526-8
  record info:
    record creation date: 190312
    record change date: 20191022031348.0
    record identifier: 978-3-030-01526-8