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Optimal and adaptive stopping based on capture times

Published online by Cambridge University Press:  14 July 2016

Norman Starr
Norman Starr*
Affiliation:
The University of Michigan
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Abstract

Independent exponential capture times are assumed for each of N prey. The payoff is the number of prey caught less a linear time cost. The optimal stopping time and value are obtained. When N is known an adaptive statistical procedure is proposed for which the expected payoff differs from the value by at most one-half plus a term which tends to zero (of order N–α, a < 1) as N → ∞.

Keywords

OPTIMAL STOPPINGADAPTIVE STOPPINGDYNAMIC PROGRAMMINGEXPONENTIAL FAILUREMARTINGALESESTIMATING POPULATION SIZEASYMPTOTIC THEORY
Type
Research Papers
Information
Journal of Applied Probability , Volume 11 , Issue 2 , June 1974 , pp. 294 - 301
Copyright
Copyright © Applied Probability Trust 1974 

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References

[1] Chow, Y. S., Robbins, H. and Siegmund, D. (1971) Great Expectations: The Theory of Optimal Stopping. Houghton Mifflin, New York.Google Scholar
[2] Darling, D. A. and Robbins, H. (1967) Finding the size of a population. Ann. Math. Statist. 38, 1392–1398.CrossRefGoogle Scholar
[3] Jolley, L. B. W. (1961) Summation of Series. (Second revised edition) Dover Publications, New York.Google Scholar