Bayesian quickest detection problems: new general results and their applications

We consider Bayesian quickest detection problems in a general setting. The first part of the talk is devoted to exact methods of solutions of these problems based on their reduction to optimal stopping problems. Here, an important role is played by the question of the existence of a Markovian sufficient statistic. We consider cases when such a statistic is given by the Kolmogorov-Shiryaev-Roberts process and provide the solutions of the corresponding optimal stopping problems. The second part of the talk is devoted to applications of the general theory to some specific problems. The results given in this part generalize well-known facts.