Optimal search strategies for Wienér processes

E. M. Klimko and James Yackel

Stochastic Processes and their Applications, 1975, vol. 3, issue 1, 19-33

Abstract: Let n independent Wiener processes be given. We assume that the following information is known about these processes; one process has drift [mu]t, the remaining n - 1 processes have drift zero, all n processes have common variance [sigma]2t, and we assume that a prior probability distribution over the n processes is given to identify the process with drift [mu]t. A searcher is permitted to observe the increments of one process at a time with the object of identifying (with probability 1 - [lambda] of correct selection) the process with drift [mu]t. 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 [mu]t.

Date: 1975
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