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Selecting the last success in Markov-dependent trials

Part of: Stochastic processes Sequential methods

Published online by Cambridge University Press:  14 July 2016

Shoou-Ren Hsiau  and
Jiing-Ru Yang
Shoou-Ren Hsiau*
Affiliation:
National Changhua University of Education
Jiing-Ru Yang*
Affiliation:
National Changhua University of Education
*
∗ Postal address: Department of Mathematics, National Changhua University of Education, Changhua, Taiwan 50058, Republic of China.
∗ Postal address: Department of Mathematics, National Changhua University of Education, Changhua, Taiwan 50058, Republic of China.
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Abstract

In a sequence of Markov-dependent trials, the optimal strategy which maximizes the probability of stopping on the last success is considered. Both homogeneous Markov chains and nonhomogeneous Markov chains are studied. For the homogeneous case, the analysis is divided into two parts and both parts are realized completely. For the nonhomogeneous case, we prove a result which contains the result of Bruss (2000) under an independence structure.

Keywords

Markov-dependent trialslast successsecretary problemoptimal stoppingbackward induction

MSC classification

Primary: 60G40: Stopping times; optimal stopping problems; gambling theory
Secondary: 62L15: Optimal stopping
Type
Research Papers
Information
Journal of Applied Probability , Volume 39 , Issue 2 , June 2002 , pp. 271 - 281
Copyright
Copyright © Applied Probability Trust 2002 

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References

Bruss, F. T. (2000). Sum the odds to one and stop. Ann. Prob. 28, 1384–1391.Google Scholar
Bruss, F. T., and Paindaveine, D. (2000). Selecting a sequence of last successes in independent trials. J. Appl. Prob. 37, 389–399.CrossRefGoogle Scholar
Chow, Y. S., Robbins, H., and Siegmund, D. (1971). Great Expectations: The Theory of Optimal Stopping. Houghton Mifflin, New York.Google Scholar
Hsiau, S. R., and Yang, J. R. (2000). A natural variation of the standard secretary problem. Statist. Sinica 10, 639–646.Google Scholar
Shiryayev, A. N. (1978). Optimal Stopping Rules (Appl. Math. 8). Springer, New York.Google Scholar