The Annals of Probability

Comments on a Problem of Chernoff and Petkau

Michael L. Hogan

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Abstract

A new method is used to study the optimal stopping set corrected for discreteness introduced by Chernoff and studied by Chernoff and Petkau. The discrete boundary is asymptotically the optimal boundary for a Wiener process translated downward by a constant amount. This amount is shown to be an "excess over the boundary" term, and this method yields it as a simple integral involving the characteristic function of the random walk.

Article information

Source
Ann. Probab., Volume 14, Number 3 (1986), 1058-1063.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176992458

Digital Object Identifier
doi:10.1214/aop/1176992458

Mathematical Reviews number (MathSciNet)
MR841604

Zentralblatt MATH identifier
0658.60070

JSTOR
links.jstor.org

Subjects
Primary: 62L15: Optimal stopping [See also 60G40, 91A60]
Secondary: 60G40: Stopping times; optimal stopping problems; gambling theory [See also 62L15, 91A60]

Keywords
Excess over the boundary optimal stopping Wiener process corrected diffusion approximations

Citation

Hogan, Michael L. Comments on a Problem of Chernoff and Petkau. Ann. Probab. 14 (1986), no. 3, 1058--1063. doi:10.1214/aop/1176992458. https://projecteuclid.org/euclid.aop/1176992458


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