Open Access
October 2011 Minimizing the time to a decision
Saul Jacka, Jon Warren, Peter Windridge
Ann. Appl. Probab. 21(5): 1795-1826 (October 2011). DOI: 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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Saul Jacka. Jon Warren. Peter Windridge. "Minimizing the time to a decision." Ann. Appl. Probab. 21 (5) 1795 - 1826, October 2011.


Published: October 2011
First available in Project Euclid: 25 October 2011

zbMATH: 1230.93100
MathSciNet: MR2884051
Digital Object Identifier: 10.1214/10-AAP737

Primary: 93E20
Secondary: 60J70

Keywords: dynamic resource allocation , multiparameter processes , optimal stochastic control , ternary majority

Rights: Copyright © 2011 Institute of Mathematical Statistics

Vol.21 • No. 5 • October 2011
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