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Expectations and variances of stopping variables in sequential selection processes

Published online by Cambridge University Press:  14 July 2016

M. Henke
M. Henke*
Affiliation:
University of Bonn
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Abstract

A sequential stochastic decision process with independent random variables is considered in which the decision maker selects a chance with a certain probability at each time period or at random times. If the decision maker has selected m chances, the process has to be stopped. The expectation and the variance of the stopping variable are determined for a finite and an infinite decision horizon.

Keywords

SEQUENTIAL SELECTION PROCESSESSTOPPING RULE PROBLEM WITH m STOPPING POINTSEXPECTATION OF STOPPING VARIABLESVARIANCES OF STOPPING VARIABLES
Type
Research Papers
Information
Journal of Applied Probability , Volume 10 , Issue 4 , December 1973 , pp. 786 - 806
Copyright
Copyright © Applied Probability Trust 1973 

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References

Breiman, L. (1964) Stopping-rule problems. In Applied Combinatorial Mathematics. Ed. Beckenbach, E. F. Wiley, New York. 284–319.Google Scholar
Chow, Y. S. and Robbins, H. (1963) On optimal stopping rules. Zeit. Wahrscheinlichkeitsth. 2, 33–49.CrossRefGoogle Scholar
Chow, Y. S., Moriguti, S., Robbins, H. and Samuels, S. M. (1964) Optimal selection based on relative rank (the “secretary problem”). Israel J. Math. 2, 81–90.CrossRefGoogle Scholar
Dynkin, E. B. and Yushkevich, A. A. (1969) Markov Processes: Theorems and Problems. Plenum Press, New York.CrossRefGoogle Scholar
Henke, M. (1970a) Optimale Stopp-und Auswahlregeln für eine Klasse stochastischer Entscheidungsprozesse. Operations Research Verfahren VII, 83–121.Google Scholar
Henke, M. (1970b) Sequentialle Auswahlprobleme bei Unsicherheit. Anton Hain Verlag, Meisenheim.Google Scholar
Henke, M. (1972) Optimal selection and stopping rules for Markovian selection processes. Submitted to Zeit. Wahrscheinlichkeitsth. Google Scholar
Kaufman, G. M. (1963) Statistical decision and related techniques in oil and gas exploration. Doctoral Dissertation Series, The Ford Foundation.Google Scholar
Lindley, D. V. (1961) Dynamic programming and decision theory. Appl. Statist. 10, 39–52.CrossRefGoogle Scholar
Macqueen, J. and Miller, R. G. (1960) Optimal persistence policies. Operations Res. 8, 362–382.CrossRefGoogle Scholar
Mosteller, C. F. (1965) Fifty Challenging Problems in Probability with Solutions. Addison-Wesley, Reading, Mass.Google Scholar