Open Access
July, 1986 Comments on a Problem of Chernoff and Petkau
Michael L. Hogan
Ann. Probab. 14(3): 1058-1063 (July, 1986). DOI: 10.1214/aop/1176992458


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.


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Michael L. Hogan. "Comments on a Problem of Chernoff and Petkau." Ann. Probab. 14 (3) 1058 - 1063, July, 1986.


Published: July, 1986
First available in Project Euclid: 19 April 2007

zbMATH: 0658.60070
MathSciNet: MR841604
Digital Object Identifier: 10.1214/aop/1176992458

Primary: 62L15
Secondary: 60G40

Keywords: Corrected diffusion approximations , excess over the boundary , Optimal stopping , Wiener process

Rights: Copyright © 1986 Institute of Mathematical Statistics

Vol.14 • No. 3 • July, 1986
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