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

Pavel V. Gapeev

LSE Research Online Documents on Economics from London School of Economics and Political Science, LSE Library

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; weighted likelihood ratio; quickest change-point (disorder); delayed optimal stopping problem; quickest change-point (disorder) detection problem; change-of-variable formula with local time on curves; free-boundary problem; (time-homogeneous) diffusion process (search for similar items in EconPapers)
JEL-codes: C1 (search for similar items in EconPapers)
Pages: 16 pages
Date: 2020-04-10
New Economics Papers: this item is included in nep-ore
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Citations: View citations in EconPapers (2)

Published in Statistical Papers, 10, April, 2020, 61(4), pp. 1529-1544. ISSN: 0932-5026

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