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On a quickest detection problem with costly information

Published online by Cambridge University Press:  14 July 2016

D. W. Balmer
D. W. Balmer*
Affiliation:
London School of Economics and Political Science
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Abstract

Problems of detecting the arrival of a ‘disorder' are of central importance in quality control. One such problem is formulated as an optimal stopping problem in which information about the process to be stopped may be bought at any time. A control policy will involve a determination of times at which information should be bought and of the time at which the process should be stopped. It is shown that in all circumstances there is a unique policy satisfying necessary conditions for optimality; the various circumstances and control policies are specified.

Keywords

QUICKEST DETECTIONCOSTLY INFORMATIONCONTROLCOSTLY SURVEILLANCEWIENER PROCESSFREE BOUNDARY PROBLEM
Type
Research Papers
Information
Journal of Applied Probability , Volume 12 , Issue 1 , March 1975 , pp. 87 - 97
Copyright
Copyright © Applied Probability Trust 1975 

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References

[1] Antelman, G. R. and Savage, I. R. (1965) Surveillance problems: Wiener processes. Naval Res. Logist. Quart. 12, 35–55.Google Scholar
[2] Bather, J. A. (1967) On a quickest detection problem. Ann. Math. Statist. 38, 711–724.Google Scholar
[3] Bather, J. A. (1972) An optimal stopping problem with costly information. Paper presented to the Joint Harvard-Imperial College Conference on Information Structure and Extensive Games .Google Scholar
[4] Bather, J. A. and Chernoff, H. (1965) Sequential decisions in the control of a spaceship. Proc. Fifth Berkeley Symp. 3, 181–207.Google Scholar
[5] Chernoff, H. (1968) Optimal stochastic control. Sankhya 30, 221–252.Google Scholar
[6] Lorden, G. (1971) Procedures for reacting to a change in distribution. Ann. Math. Statist. 42, 1897–1908.Google Scholar
[7] Mandl, P. (1968) Analytical Treatment of One-dimensional Markov Processes. Academia, Prague, and Springer-Verlag, Berlin.Google Scholar
[8] Shiryaev, A. N. (1963) On optimum methods in quickest detection problems. Theor . Probability Appl. 8, 22–46.Google Scholar