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

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  • Pavel V. Gapeev

    (London School of Economics)

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.

Suggested Citation

  • Pavel V. Gapeev, 2020. "On the problems of sequential statistical inference for Wiener processes with delayed observations," Statistical Papers, Springer, vol. 61(4), pages 1529-1544, August.
    • Handle: RePEc:spr:stpapr:v:61:y:2020:i:4:d:10.1007_s00362-020-01178-0
    DOI: 10.1007/s00362-020-01178-0
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    References listed on IDEAS

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    Cited by:

    1. Buonaguidi, B., 2022. "The disorder problem for diffusion processes with the ϵ-linear and expected total miss criteria," Statistics & Probability Letters, Elsevier, vol. 189(C).
    2. Georgy Sofronov & Martin Wendler & Volkmar Liebscher, 2020. "Editorial for the special issue: Change point detection," Statistical Papers, Springer, vol. 61(4), pages 1347-1349, August.

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