Optimal search strategies for Wienér processes

Let n independent Wiener processes be given. We assume that the following information is known about these processes; one process has drift μt, the remaining n - 1 processes have drift zero, all n processes have common variance σ²t, and we assume that a prior probability distribution over the n processes is given to identify the process with drift μt. A searcher is permitted to observe the increments of one process at a time with the object of identifying (with probability 1 - λ of correct selection) the process with drift μt.The authors define a natural class of search strategies and show that the strategy within this class which minimizes the total search time is the strategy which, whenever possible, searches the process which currently has the largest posterior probability of being the one with drift μt.