Search models

Mathematical models have been proposed for oil exploration and other kinds of search. They can be used to estimate the amount of undiscovered resources or to investigate optimal stopping times for the search. Here the paper considers a continuous search for hidden objects using a model which represents the number and values of the objects by mixtures of Poisson processes. The flexibility of the model and its complexity depend on the number of components in the mixture. In simple cases, optimal stopping rules can be found explicitly and more general qualitative results can sometimes be obtained.