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Some asymptotic results for optimal stopping based on capture times

Published online by Cambridge University Press:  14 July 2016

Robert L. Wardrop
Robert L. Wardrop*
Affiliation:
University of Wisconsin-Madison
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Abstract

A region contains n prey labeled 1, 2, …, n. Prey i is captured at the random time Zi; where Z1, Z2, …, Zn are i.i.d. with distribution function F. The statistician must decide when to stop searching, with the goal of maximizing the number of prey captured minus a linear time cost, c. The optimal strategy and its expected payoff are studied asymptotically as n, c →∞, for F a beta or Weibull distribution.

Keywords

OPTIMAL STOPPINGBROWNIAN MOTIONWEAK CONVERGENCEUNIFORM INTEGRABILITY
Type
Research Papers
Information
Journal of Applied Probability , Volume 13 , Issue 4 , December 1976 , pp. 741 - 750
Copyright
Copyright © Applied Probability Trust 1976 

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References

[1] Billingsley, P. (1968) Convergence of Probability Measures. Wiley, New York.Google Scholar
[2] Brillinger, D. R. (1969) An asymptotic representation of the sample distribution function. Amer. Math. Soc. Bull. 75, 545–547.Google Scholar
[3] Dvoretzky, A., Kiefer, J. and Wolfowitz, J. (1956) Asymptotic minimax character of the sample distribution function and of the classical multinomial estimator. Ann. Math. Statist. 27, 642–669.Google Scholar
[4] Ross, S. (1971) Infinitesimal look-ahead stopping rules. Ann. Math. Statist. 42, 297–303.Google Scholar
[5] Shepp, L. A. (1969) Explicit solutions to some problems of optimal stopping. Ann. Math. Statist. 40, 993–1010.Google Scholar
[6] Starr, N. (1974) Optimal and adaptive stopping based on capture times. J. Appl. Prob. 11, 294–301.Google Scholar
[7] Starr, N., and Woodroofe, M. (1974) Gone Fishin': Optimal Stopping Based on Catch Times. The University of Michigan Technical Report # 33, Department of Statistics.Google Scholar
[8] Wardrop, R. (1975) Some Exact Results for Optimal Stopping Based on Capture Times. Technical Report # 432, University of Wisconsin-Madison Statistics Department.Google Scholar