Stochastic Disorder Problems

• Main Author: Shiryaev, Albert N. (Author, http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2019.
• Edition: 1st ed. 2019.
• Series: Probability Theory and Stochastic Modelling, 93
• Subjects: System theory.; Probabilities.; Statistics .; Economics, Mathematical .; Finance-Mathematics.; Systems Theory, Control.; Probability Theory and Stochastic Processes.; Statistical Theory and Methods.; Quantitative Finance.; Financial Mathematics.; Bayesian Inference.

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 a...

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.