On the problems of sequential statistical inference for Wiener processes with delayed observations

Pavel V. Gapeev ()
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Pavel V. Gapeev: London School of Economics

Statistical Papers, 2020, vol. 61, issue 4, No 8, 1529-1544

Abstract: Abstract We study the sequential hypothesis testing and quickest change-point (or disorder) detection problems with linear delay penalty costs for observable Wiener processes under (constantly) delayed detection times. The method of proof consists of the reduction of the associated delayed optimal stopping problems for one-dimensional diffusion processes to the equivalent free-boundary problems and solution of the latter problems by means of the smooth-fit conditions. We derive closed-form expressions for the Bayesian risk functions and optimal stopping boundaries for the associated weighted likelihood ratio processes in the original problems of sequential analysis.

Keywords: Sequential testing problem; Quickest change-point (disorder) detection problem; Weighted likelihood ratio; (Time-homogeneous) diffusion process; Delayed optimal stopping problem; Free-boundary problem; Change-of-variable formula with local time on curves; Primary 60G40; 60J60; 34K10; Secondary 62M20; 62C10; 62L15 (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s00362-020-01178-0

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