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Optimal search for a randomly moving object in a special case

Published online by Cambridge University Press:  14 July 2016

Olavi Hellman
Olavi Hellman*
Affiliation:
University of Turku, Finland
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Abstract

Search for an object whose motion is a symmetrical two-dimensional diffusion process is considered in the case where a given amount of search of constant density is distributed, during a given interval of time, over a fixed circular area. An expression for the probability of detection of the object during this interval of time is derived in the special case where the location of the object at time zero is given. The application of this expression would involve numerical work.

Type
Short Communications
Information
Journal of Applied Probability , Volume 8 , Issue 3 , September 1971 , pp. 606 - 611
Copyright
Copyright © Applied Probability Trust 1971 

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References

[1] Arkin, V. (1964) Uniformly optimal strategies in search problems. Theor. Probability Appl. 9, 674–680.CrossRefGoogle Scholar
[2] Hellman, O. (1969) On the optimal search for a randomly moving target. ORC 69–33, Operations Research Center, Univ. of California, Berkeley.Google Scholar
[3] Hellman, O. (1970) On the effect of a search upon the probability distribution of a target whose motion is a diffusion process. Ann. Math. Statist. 41, 1717–1724.Google Scholar
[4] Hellman, O. (1967) Bayesian expression for the probability that a searcher will find a target. Unternehmensforschung 12, 178–179.Google Scholar
[5] Hellman, O. (1970) On the determination of the optimal search density for targets whose motion is a diffusion process. ORC 70–14, Operations Research Center, Univ. of California, Berkeley.Google Scholar