Comments on a problem of Chernoff and Petkau
type: Item
instance of: scholarly article
title: Comments on a problem of Chernoff and Petkau
zbMATH Open document ID: 0658.60070
author: Michael L. Hogan
published in: The Annals of Probability
publication date: 1986-01-01T00:00:00Z
review text: A new method is used to study the optimal stopping set corrected for discreteness introduced by \textit{H. Chernoff} [Ann. Math. Statistics 36, 55-68 (1965; Zbl 0246.62084)] and studied by \textit{H. Chernoff} and \textit{A. J. Petkau} [Ann. Probab. 4, 875-889 (1976; Zbl 0347.62064)]. 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.
Mathematics Subject Classification ID: 60G40
Mathematics Subject Classification ID: 62L15
zbMATH DE Number: 4076212
zbMATH Keywords: corrected diffusion approximation
zbMATH Keywords: optimal stopping set
zbMATH Keywords: discrete boundary
zbMATH Keywords: optimal boundary
zbMATH Keywords: Wiener process
zbMATH Keywords: excess over the boundary
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aop/1176992458
OpenAlex ID: W2011632336
DOI: 10.1214/AOP/1176992458
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description: scientific article; zbMATH DE number 4076212