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Optimal stopping problems for Brownian motion

Published online by Cambridge University Press:  01 July 2016

John Bather
John Bather*
Affiliation:
University of Sussex
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Extract

This paper is concerned with the general problem of choosing an optimal stopping time for a Brownian motion process, where the cost associated with any trajectory depends only on its final time and position.

Type
Research Article
Information
Advances in Applied Probability , Volume 2 , Issue 2 , Autumn 1970 , pp. 259 - 286
Copyright
Copyright © Applied Probability Trust 1970 

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References

[1] Bather, J. A. (1962) Bayes procedures for deciding the sign of a normal mean. Proc. Camb. Phil. Soc. 58, 599–620.Google Scholar
[2] Breakwell, J. V. and Chernoff, H. (1964) Sequential tests for the mean of a normal distribution II (large t) , Ann. Math. Statist. 35, 162–173.Google Scholar
[3] Chernoff, H. (1961) Sequential tests for the mean of a normal distribution. Proc. Fourth Berkeley Symp. 1, 79–91. University of California Press.Google Scholar
[4] Chernoff, H. (1965) Sequential tests for the mean of a normal distribution III (small t) . Ann. Math. Statist. 36, 28–54.Google Scholar
[5] Chernoff, H. (1965) Sequential tests for the mean of a normal distribution IV (discrete case). Ann. Math. Statist. 36, 55–68.Google Scholar
[6] Chernoff, H. (1968) Optimal stochastic control. Sankhya 30, 221–252.Google Scholar
[7] Doob, J. L. (1955) A probability approach to the heat equation. Trans. Amer. Math. Soc. 80, 216–280.CrossRefGoogle Scholar
[8] Dynkin, E. B. (1963) Optimal selection of stopping time for a Markov process. Dokl. Akad. Nauk, USSR 150, 238–240. (English translation in Soviet Math. 4, 627–629).Google Scholar
[9] Grigelionis, B. I. and Shiryaev, A. N. (1966) On Stefan's problem and optimal stopping rules for Markov processes. Theor. Probability Appl. 11, 541–558.CrossRefGoogle Scholar
[10] Hartman, P. and Winter, A. (1950) On the solutions of the equation of heat conduction. Amer. J. Math. 72, 367–395.Google Scholar
[11] Taylor, H. M. (1968) Optimal stopping in a Markov process. Ann. Math. Statist. 39, 1333–1344.Google Scholar