Bayesian Sequential Hypothesis Testing

We consider the Bayesian sequential detection problem for general observation processes with a continuous time parameter. Primary emphasis is placed on first exit policies and their generic optimality. A new geometric formulation and solution to the existence and uniqueness of the optimal first exit policy will be given as well as an explicit constructive algorithm for its computation. We will apply these resuits to the problem of Bayesian sequential detection for diffusion-type observations although our methods and results generalize to problems of optimal stopping and decision for partially observed Markov chains where the observation processes are of the diffusion or point process type. These results will appear elsewhere.