Hostname: page-component-586b7cd67f-t7czq Total loading time: 0 Render date: 2024-11-22T04:52:39.084Z Has data issue: false hasContentIssue false

Expectations and variances of stopping variables in sequential selection processes

Published online by Cambridge University Press:  14 July 2016

M. Henke*
Affiliation:
University of Bonn

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.

Type
Research Papers
Copyright
Copyright © Applied Probability Trust 1973 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Breiman, L. (1964) Stopping-rule problems. In Applied Combinatorial Mathematics. Ed. Beckenbach, E. F. Wiley, New York. 284319.Google Scholar
Chow, Y. S. and Robbins, H. (1963) On optimal stopping rules. Zeit. Wahrscheinlichkeitsth. 2, 3349.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, 8190.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, 83121.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, 3952.CrossRefGoogle Scholar
Macqueen, J. and Miller, R. G. (1960) Optimal persistence policies. Operations Res. 8, 362382.CrossRefGoogle Scholar
Mosteller, C. F. (1965) Fifty Challenging Problems in Probability with Solutions. Addison-Wesley, Reading, Mass.Google Scholar