The Annals of Applied Probability

Minimizing the time to a decision

Saul Jacka, Jon Warren, and Peter Windridge

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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.

Article information

Ann. Appl. Probab., Volume 21, Number 5 (2011), 1795-1826.

First available in Project Euclid: 25 October 2011

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Zentralblatt MATH identifier

Primary: 93E20: Optimal stochastic control
Secondary: 60J70: Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.) [See also 92Dxx]

Optimal stochastic control dynamic resource allocation multiparameter processes ternary majority


Jacka, Saul; Warren, Jon; Windridge, Peter. Minimizing the time to a decision. Ann. Appl. Probab. 21 (2011), no. 5, 1795--1826. doi:10.1214/10-AAP737.

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