Minimizing the time to a decision

Details Minimizing the time to a decision Minimizing the time to a decision

2009-11-28

arxiv.org/abs/0911.5413v3

Annals of Applied Probability 2011, Vol. 21, No. 5, 1795-1826

Mathematics

Probability

Published in at http://dx.doi.org/10.1214/10-AAP737 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Inst

Scientific paper

10.1214/10-AAP737

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.

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