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Minimizing the time to a decision. (English) Zbl 1230.93100

Summary: Suppose we have three independent copies of a regular diffusion on [0, 1] with absorbing boundaries. Of these diffusions, either at least two are absorbed at the upper boundary or at least two at the lower boundary. In this way, they determine a majority decision between 0 and 1. We show that the strategy that always runs the diffusion whose value is currently between the other two reveals the majority decision whilst minimizing the total time spent running the processes.

MSC:

93E20 Optimal stochastic control
60J70 Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.)
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