The models of quickest detection deal with the on-line problems in which probabilistic character of the data changes during observations. In the simplest situations there is a hidden parameter theta such that before theta observations have “normal” distribution and after theta the observations have some “nonnormal” component. The quickest detection (QD) problems consist in quickest detection of a hidden time theta, with minimal false alarms. At present there exists very intensive literature on the QD-problems. The corresponding theories are based on the stochastic calculus and the theory of optimal stopping rules which define the stopping time when the alarm signal should be declared.

Lectures 1-2. Probabilistic models in the discrete-time and continuous-time QD-problems. Formulations of the Bayesian and minimax problems and their reduction to the special optimal stopping problems.

Lectures 3-4. Basic results of the general theory of optimal stopping for cases of discrete and continuous time. Martingale and Markovian approaches.

Lectures 5-6. Basic models of quickest detection (Shewhart, Page, models A, B, C, D, …) and their reduction to special problems of optimal stopping.

Lectures 7-8. Detailed analysis of models A, B, C, D for the Brownian motion with changing drift.

Lectures 9-10. Sequential testing of two and more hypotheses and problems of estimation of the drift for a Brownian motion and fractional Brownian motion. Application to Finance (Buy-and-Hold, trading of the bubble).