Stochastic Disorder Problems

by Albert N. Shiryaev

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.

420 pages, Paperback

Published March 15, 2019