A model for decision problems with continuous time parameter

The concept of statistical decision theory concerning sequential observations is generalized to decision problems, which are based upon a continuous stochastic process.

In this model decision functions are introduced, consisting of a stopping time and a terminal decision rule. A method of discretization shows the connections between the discrete sequential and the continuous model. Concerning Bayes problems we find, that under certain assumptions the decision problem can be viewed as an optimal stopping problem with continuous time parameter.